Topic: Math/Physic/Economic/Statistic Problems

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3.2

MBA 791. ANALYSIS USING PROBABALISTIC AND SIMULATION MODELS WEEK 3
COMPUTER SIMULATION MODELING -- Objectives of this week:
Introduction to simulation modeling
Demonstrate process of building a core model and working with that model to answer business questions
and demonstrate =RAND()
these Excel =IF
capabilities: Data Table tool -- used to "replicate" simulation models
=FREQUENCY -- used to organize the results of replicating the model into a frequency table
=VLOOKUP -- for discrete random variables
=NORMINV --for a normal random variable
and formulas for --Uniform random variable: = Min + (Max-Min)*RAND()
--Exponential random variable: = - (mean)*LN(RAND())
DEF: Simulation Modeling and Analysis:
DEFINITION: USING TECHNOLOGY TO IMITATE (SIMULATE) THE OPERATION/BEHAVIOR OF A BUSINESS PROCESS OR SYSTEM
PRODUCING SIMULATED RESULTS OVER SOME TIME PERIOD (DAYS, WEEKS, MONTHS, YEARS, ETC.)
--USED FOR SITUATIONS IN WHICH KEY PARAMETERS ARE PROBABLISTIC (VALUES OCCUR RANDOMLY ACCORDING TO SOME DISTRIBUTION)
AND THE IMPACT OF THIS VARIATION IS IMPORTANT TO UNDERSTAND OR ANALYZE (just using average values is NOT adequate)
Production processes
Inventory processes Why? Need to
Financial risk investments (1) analyze/understand current design; OR (2) analyze/compare alternative design options
Health care processes Using the model, simulate behavior, and estimate the key output measures
-- two types of objective measures
. . . A. Costs: fixed costs, wages, O/H, supplies, waiting/delay costs (lost production, lost customers)
B. Benefits: product/service revenues or profits, value to next operation for internal customer
achievement of targets, e.g., max customer waiting, acceptable slack time for workers
Analysis with Simulation Modeling Process: e.g., manufacturing, service, sales, …
BUSINESS ISSUE: A particular business process KEY MEASURES OF PROCESS BEHAVIOR -- objective measures:
Input/output flows QUESTIONS ANSWERS
constant or variable rate task How long (start to finish)? Not a single number -- rather, a distribution
constant or variable properties task How much cost? Not a single number -- distribution
independent or dependent task How much delay? Not a single number -- distribution
task How much customer wait? Not a single number -- distribution
Tasks or subprocesses task What is output quality Not a single number -- distribution
constant or variable time to completion What is revenue each day? Not a single number -- distribution
constant or variable quality of output . . .
constant or variable cost of completing the task If process is changed, how do the above
distributions change?
Study and understand process/system
leading to "problem definition"
Problem Definition
BUSINESS PROBLEM: BusQues(s): Can we develop a better understanding of this process? What if something changes?
and (maybe) What is the evaluation/comparison of several options for this process?
Decisions: Maybe NONE. Maybe the possible changes.
Obj measure(s): The distribution of one, or often more than one, specific measures
e.g., avg, stdev, and 90%tile of total cost/overall time /overall revenue …)
BUSINESS DATA: gather data on process properties Constraints: the structure of the process/system and estimates of "how something works" and estimates of distributions
ANALYSIS:
1. Build a CORE Model. CORE MODEL -- DESCRIBES HOW BUSINESS PROCESS WORKS -- SEQUENCE OF ACTIONS AND RESULTS
CORE Model: Operation of the bus process for one time or over one hour or day or … Data input cells
constant in value NEW SIMULATION MODEL FEATURE! -- Green cell
variable in value (specify a probability distribution -- formula)
Decision cells (e.g., possible adjustments or changes to the business process)
may not involve decisions -- modeling to understand a current unchanged process
perhaps alternative process "settings" or alternative designs MAYBE NO YELLOW CELLS IN MODEL
Output cells -- containing formulas
calculating values of key properties of the flows and of subprocesses
Objective cell(s)
calculating values of requested objective measures (one or more)
2. Test/Validate the core model
Very important due to often high level of model complexity.
Start simple and build complexity gradually. NEW TYPE OF MODEL MANIPULATION!
Not "Solver" Not "SolverTable"
3. Replicate the core model to "simulate" (1) many times of process completion (behavior) or (2) the process being used many hours or days
maybe 1,000 or more times. -->like actually observing a large sample of this business process
With this large sample, now can describe/estimate the distributions of the key objective measures
Calculate summary values like sample mean, stdev, percentiles, Q1, Q3, etc. -- use as estimates of true mean, stdev, percentiles, …
Develop a frequency table of classes and proportion of values in each.
Develop graphs/figures depicting the full distribution (histograms).
Sometimes this distribution is called the RISK PROFILE of the objective measures of this business sytem or business process.
IF ASKED TO ANALYZE DECISION OPTIONS:
Make a change to the process (to the core model) and perform the replications again. Record new values of the measures. Organize and compare.
4. Organize all the results into one or several RESULTS TABLES and graphs -- to present/show conclusions and insights.
BUSINESS CONCLUSIONS (INSIGHTS) AND PERHAPS RECOMMENDATIONS
Business language "answers" to the Business Question.
LET'S SHOW AND LEARN WITH SOME EXAMPLES OF ANALYSIS USING SIMULATION MODELS

3.3.1

SIMULATION MODELING EXAMPLE Demonstrate Analysis with Simulation Models using Excel capabilities: =RAND, =IF, Data Table, =FREQUENCY
Similar to Example 1 in chapter 12 of text. Issue: Process -- A coin-flipping game
Problem Definition: BusQuestion: What are the results of playing this game? Can I get a better understanding of this game and its outcomes?
Decision: After the better understanding --> Yes or No -- play the game or not. (No decision in the Core Model.)
Objective Measure: Winnings ($) -- avg, stdev, 5 percentile, 95 percentile, min, max, risk of "big" loss: more than $10? Perhaps risk profile of winnings. Perhaps, Other?
Constraints: Rules of the game. Can't quit in middle of game.
Data: Play of Game: Repeated flipping of a coin until the difference
between the # H and # T is 3. KEY FUNCTION USED IN ALL EXCEL SIMULATION MODELS:
Cost of Game: $1 for each flip of the coin. How do we generate the random results? Of each flip?
Payoff of Game: $8 at the end of the game. Use =RAND() -- produces a random number between 0.0000 and 0.9999
THUS: You win $ if the number of flips is < 8 (Max win is $5). Each result is equally likely. Thus, a 50 percent chance that the
You break even if the number of flips is = 8. result is 0.0000 to 0.4999 & 50% chance it is 0.5000 to 0.99999 unless you turn off automatic recalculation
You lose $ if the number of flips is > 8 (max. loss is very high). NOTE: =RAND() is a volatile function. Re-executes with each ss execution (under Formula tab)
Analysis: Build and then Use a Simulation Model (spreadsheet) Use =IF(condition, execute if true, execute if false)
1. Build a CORE model of one play of the game.
Process is successive flips of coin -- use rows for each flip and use columns for recording results and game status.
Let's set up some total # that we should hardly ever reach -- try 50. Note: Could have used =RAND() within a flip result cell with formula: =IF(RAND()<0.5,"Tails","Heads") e.g.
Tails
CORE Cost of Each Flip= $1 Coin Input Game Results:
MODEL: STOP if H-T Diff = 3 Pr(T) = 0.5 # Flips: Winnings:
(ea row ~ one flip) Payoff at end = $8 Total Total 9 -$1
FLIP RAND() RESULT Heads Tails Diff Stop?
In simulation modeling (on spreadsheets) we'll continue to use blue (data input cells), yellow (decision cell), gray (ouput cells with formulas), orange (key output cell calculation), and now green (random variable). NOTE: Often there is NO decision. 1 0.5694207899 Heads 1 0 1
2 0.2401681833 Tails 1 1 0
3 0.1891952209 Tails 1 2 1
4 0.7753546019 Heads 2 2 0
5 0.0570574658 Tails 2 3 1
6 0.5987050424 Heads 3 3 0
7 0.833934087 Heads 4 3 1
8 0.67366571 Heads 5 3 2
9 0.7164622187 Heads 6 3 3 stop
10 0.5557464516 Heads 7 3 4 na
11 0.0963214083 Tails 7 4 3 na
12 0.8728915173 Heads 8 4 4 na
13 0.601140343 Heads 9 4 5 na
14 0.5789102132 Heads 10 4 6 na
15 0.865783492 Heads 11 4 7 na
16 0.022629617 Tails 11 5 6 na
17 0.1751174956 Tails 11 6 5 na
18 0.8841210059 Heads 12 6 6 na
19 0.7452062804 Heads 13 6 7 na
20 0.1514731447 Tails 13 7 6 na
21 0.801257185 Heads 14 7 7 na
22 0.4588384139 Tails 14 8 6 na
23 0.8227670762 Heads 15 8 7 na
24 0.6011312104 Heads 16 8 8 na
25 0.7673032502 Heads 17 8 9 na
26 0.2772313145 Tails 17 9 8 na
27 0.2450797073 Tails 17 10 7 na
28 0.5216810716 Heads 18 10 8 na
29 0.9087072885 Heads 19 10 9 na
30 0.3193699949 Tails 19 11 8 na
31 0.8625515845 Heads 20 11 9 na
32 0.9817340712 Heads 21 11 10 na
33 0.1668772719 Tails 21 12 9 na
34 0.0966903984 Tails 21 13 8 na
35 0.6432708066 Heads 22 13 9 na
36 0.0777427752 Tails 22 14 8 na
37 0.5507169976 Heads 23 14 9 na
38 0.0127172199 Tails 23 15 8 na
39 0.4651327773 Tails 23 16 7 na
40 0.7066486946 Heads 24 16 8 na
41 0.4545214264 Tails 24 17 7 na
42 0.2321398322 Tails 24 18 6 na
43 0.4651582249 Tails 24 19 5 na
44 0.0591048317 Tails 24 20 4 na
45 0.9874144417 Heads 25 20 5 na
46 0.1798531088 Tails 25 21 4 na
47 0.9962987835 Heads 26 21 5 na
48 0.2610618101 Tails 26 22 4 na
49 0.8523408757 Heads 27 22 5 na
50 0.5228282848 Heads 28 22 6 na

3.3.3

This is the core model of one play of the game.
2. Test and validate it.
3. Simulate or replicate the game many times.
Now, let's simulate playing this game many times
so we can see the various # flips and winnings,
i.e, the "distribution" of possible game results
Can Use Excel's tool "Data Table":
Play # Flips Winnings USING DATA TABLE. (1) Set up a table for results. In first column enumerate the # of plays. In first row, enter cell references to core model of key ouputs of game. (2) Highlight the table including first column and top row (not labels row). (3) Select Data, What If, Data Table. (4) In the pop-up menu, enter nothing the row input cell, and enter any blank cell in the column input cell. (5) Execute with "OK." (Need automatic calculation under Formulas.)
ERROR:#REF! ERROR:#REF!
1 19 -11
2 9 -1
3 7 1
4 15 -7
5 25 -17
6 3 5
7 5 3
8 5 3
9 3 5
10 7 1
11 9 -1
12 5 3
13 17 -9
14 5 3
15 5 3
16 7 1
17 9 -1
18 5 3
19 17 -9
20 27 -19
21 5 3
22 3 5
23 19 -11
24 37 -29
25 13 -5
Avgs: ERROR:#REF! -$3.24 Notice the variability.
of this value as you
repeatedly do 25 simulations
CONCLUSION:
NEED A LARGE NUMBER OF SIMULATIONS
FOR KEY OUTPUTS TO "STABILIZE"
Typical -- 1,000 replications.
labels
<= -$20
1,000 Replications of Game: Want a large enough sample such that the key measures are stable (don't change very much with successive samples). <= -$15
Winnings <= -$10
$0 4. Now let's summarize our model output: <= -$5
1 -9 <= 0
2 3 Avg Winnings: -$1.19 <= $5
3 1 Median Winnings: $1.00 Review the formulas in cells F79 to F86 to learn
4 5 Stdev of Winnings: $7.18 about Excel functions for these summary statistics.
5 -3 5 Percentile Winnings: -$15
6 -15 95 Percentile Winnings: $5
7 1 Min Winning: -$41
8 3 Max Winning: $5
9 5 Prob (Win = $5): 0.25 Show results as a graph -- the risk profile of winnings
10 3 Prob(loss>=$10): 0.12
11 -1 Can show results in a graph (histogram)
12 5 Classes: Count Prop To use =FREQUENCY
13 5 -20 21 ERROR:#DIV/0! (1) Set up the table by defining classes & entering
14 -1 -15 36 ERROR:#DIV/0! the upper value of each class in the first column.
15 -1 -10 60 ERROR:#DIV/0! (2) Highlight the second column where the count values (the frequencies) will go
16 1 -5 140 ERROR:#DIV/0! (3) Key in =FREQUENCY(cells containing all the values,cells defining the classes)
17 5 0 172 ERROR:#DIV/0! (4) Don't execute with 'Enter' -- rather execute with "Shft-Ctrl-Enter"
18 -7 5 571 ERROR:#DIV/0!
19 3 Total: 1000 ERROR:#DIV/0! ~ 60 percent chance of winning (some amounts)
20 3 Answer: Describe the risk profile, the probability distribution of the key output(s) referring to summary tables and graphs. ~ 26 percent chance of losing $5 or more
21 -3 Max winnings $5 while minimum is as much as $40 Loss Should have positive winnings between 55 and 60 percent of games ~12 percent chance of losing $10 or more
22 1 Average winnings are approximate: loss of more than $1. Losing more than $10 --about a 11 percent chance.
23 5
24 -15 Volatile functions such as =RAND() re-execute for any worksheet execution in the whole Excel file.
25 -1 It is possible to "turn off" this re-execution -- "freeze" one set of results.
26 -15 There are two ways. After your work is complete, will ALWAYS do one of the following:
27 5 (1) Go to Formulas, Calculation, Calculation Options, and select Manual.
28 3 This turns off automatic calculation for all worksheets of that file and any other Excel files open.
29 -1 Go back to "Automatic" when desired.
30 3 (2) Once you are satisfied with the model and its results, can "freeze" the random results. recommended
31 5 Do this by highlighting the column(s) of data table results, copying, paste special, values, OK.
32 1 NOTE: Do not "freeze" the core model or the cells at the top of the data table referring back to
33 -7 the core model.
34 -9
35 -11
36 -5
37 -27
38 1
39 1
40 3
41 5
42 -33
43 -9
44 5
45 5
46 5
47 3
48 5
49 5
50 5
51 -3
52 -3
53 5
54 1
55 -3
56 5
57 5
58 -3
59 5
60 -9
61 5
62 5
63 1
64 5
65 -5
66 -5
67 1
68 -5
69 -13
70 -7
71 3
72 -7
73 -1
74 3
75 3
76 -5
77 -1
78 -39
79 -5
80 1
81 3
82 -1
83 5
84 1
85 1
86 -3
87 -9
88 -3
89 5
90 -7
91 -11
92 -25
93 -11
94 -9
95 -1
96 -11
97 -9
98 -15
99 5
100 -3
101 -11
102 -1
103 -19
104 -1
105 -11
106 1
107 3
108 5
109 1
110 1
111 3
112 3
113 5
114 5
115 -11
116 3
117 -3
118 5
119 1
120 1
121 5
122 3
123 1
124 3
125 -1
126 5
127 5
128 -1
129 3
130 -9
131 3
132 -5
133 -1
134 5
135 3
136 1
137 5
138 1
139 -17
140 1
141 -5
142 -19
143 -1
144 3
145 -13
146 5
147 -13
148 3
149 3
150 -5
151 -3
152 5
153 -5
154 1
155 5
156 -9
157 3
158 1
159 -1
160 5
161 3
162 3
163 1
164 -3
165 3
166 -7
167 5
168 5
169 1
170 3
171 5
172 -5
173 -11
174 -3
175 -1
176 -3
177 -5
178 -1
179 5
180 5
181 3
182 -3
183 -13
184 -1
185 1
186 -13
187 1
188 3
189 -3
190 1
191 3
192 1
193 -1
194 5
195 -19
196 -1
197 5
198 5
199 -1
200 -13
201 5
202 5
203 -1
204 3
205 -13
206 -1
207 5
208 5
209 -17
210 5
211 -5
212 -3
213 -1
214 1
215 -1
216 3
217 -11
218 -15
219 3
220 -7
221 1
222 -3
223 1
224 -17
225 -5
226 -7
227 -11
228 5
229 -5
230 3
231 3
232 5
233 -1
234 -7
235 -5
236 -3
237 -3
238 3
239 -17
240 3
241 5
242 1
243 1
244 -5
245 -5
246 3
247 -1
248 3
249 5
250 3
251 -13
252 3
253 1
254 -5
255 -1
256 -11
257 5
258 3
259 -9
260 -5
261 -5
262 -1
263 -3
264 5
265 3
266 5
267 -3
268 -9
269 -1
270 1
271 -7
272 3
273 -9
274 3
275 -23
276 3
277 5
278 1
279 -11
280 5
281 5
282 -7
283 5
284 5
285 5
286 3
287 5
288 -3
289 5
290 5
291 5
292 -3
293 -7
294 -19
295 -9
296 -7
297 5
298 -1
299 3
300 3
301 3
302 -7
303 5
304 -3
305 3
306 5
307 -9
308 1
309 -17
310 -5
311 1
312 3
313 -1
314 -5
315 1
316 1
317 -5
318 -1
319 5
320 5
321 5
322 -1
323 5
324 5
325 3
326 5
327 -11
328 -11
329 5
330 5
331 -1
332 3
333 5
334 5
335 -3
336 1
337 3
338 5
339 -15
340 -7
341 -5
342 1
343 -1
344 -1
345 -5
346 -5
347 5
348 -1
349 3
350 3
351 5
352 3
353 5
354 3
355 5
356 -5
357 -29
358 3
359 -1
360 3
361 1
362 5
363 3
364 5
365 3
366 3
367 1
368 5
369 5
370 3
371 3
372 5
373 3
374 -11
375 5
376 -23
377 -5
378 3
379 3
380 1
381 5
382 -19
383 1
384 -3
385 -11
386 3
387 3
388 3
389 5
390 1
391 3
392 5
393 3
394 -7
395 3
396 1
397 -1
398 -1
399 -7
400 3
401 5
402 5
403 1
404 -3
405 5
406 3
407 3
408 5
409 1
410 -3
411 -9
412 1
413 -1
414 3
415 -3
416 -1
417 5
418 3
419 -3
420 3
421 -1
422 -7
423 1
424 5
425 -11
426 5
427 3
428 5
429 -5
430 5
431 3
432 5
433 3
434 1
435 1
436 -11
437 3
438 5
439 -11
440 1
441 1
442 1
443 1
444 -39
445 5
446 3
447 1
448 3
449 -5
450 1
451 -11
452 -5
453 5
454 3
455 -13
456 -3
457 3
458 -7
459 -1
460 5
461 -17
462 5
463 -9
464 -3
465 3
466 5
467 -13
468 3
469 5
470 -3
471 -35
472 -1
473 5
474 3
475 3
476 5
477 -3
478 3
479 5
480 5
481 -3
482 -1
483 -9
484 -5
485 -9
486 3
487 -5
488 5
489 3
490 5
491 -5
492 1
493 5
494 1
495 5
496 1
497 -7
498 5
499 -11
500 3
501 5
502 -1
503 -3
504 5
505 5
506 -7
507 -1
508 5
509 5
510 3
511 -23
512 5
513 1
514 5
515 -7
516 -7
517 -9
518 -11
519 3
520 -1
521 1
522 5
523 5
524 -1
525 5
526 -13
527 -1
528 -3
529 5
530 5
531 -1
532 -7
533 -1
534 5
535 5
536 5
537 5
538 5
539 1
540 -9
541 -5
542 1
543 1
544 -5
545 -7
546 5
547 5
548 3
549 3
550 -1
551 3
552 -5
553 -1
554 -5
555 -15
556 3
557 1
558 -1
559 3
560 5
561 5
562 1
563 1
564 -1
565 1
566 -3
567 1
568 -1
569 3
570 -1
571 5
572 5
573 -5
574 5
575 5
576 3
577 3
578 -19
579 3
580 3
581 3
582 -13
583 -1
584 -1
585 3
586 -1
587 5
588 -1
589 -1
590 5
591 -1
592 -5
593 3
594 -3
595 5
596 -9
597 -3
598 -1
599 1
600 3
601 -1
602 -3
603 5
604 5
605 5
606 -1
607 1
608 -11
609 -1
610 -1
611 3
612 3
613 1
614 -13
615 -21
616 -9
617 5
618 5
619 3
620 -11
621 -1
622 3
623 5
624 5
625 -1
626 5
627 1
628 3
629 3
630 1
631 -3
632 -13
633 1
634 1
635 3
636 5
637 -1
638 3
639 1
640 -15
641 3
642 1
643 -7
644 -1
645 -35
646 5
647 -3
648 3
649 -33
650 1
651 5
652 3
653 -25
654 5
655 5
656 3
657 5
658 5
659 5
660 5
661 -1
662 1
663 1
664 -19
665 3
666 5
667 -29
668 -3
669 -9
670 5
671 1
672 3
673 3
674 3
675 -15
676 3
677 -13
678 1
679 3
680 -13
681 5
682 1
683 5
684 -15
685 -1
686 -3
687 3
688 5
689 1
690 3
691 5
692 5
693 3
694 5
695 3
696 1
697 -13
698 -7
699 -9
700 -7
701 -5
702 3
703 1
704 -1
705 -1
706 5
707 1
708 3
709 5
710 -5
711 -1
712 5
713 3
714 5
715 -1
716 3
717 5
718 5
719 5
720 -5
721 -5
722 3
723 3
724 1
725 -1
726 -3
727 5
728 -19
729 3
730 5
731 3
732 -3
733 -7
734 -3
735 5
736 3
737 1
738 1
739 -1
740 3
741 -5
742 5
743 -13
744 5
745 -11
746 -5
747 5
748 -5
749 1
750 -17
751 -1
752 5
753 5
754 3
755 -13
756 3
757 -7
758 3
759 1
760 -15
761 -21
762 5
763 1
764 -9
765 -11
766 3
767 3
768 1
769 5
770 5
771 -13
772 -37
773 5
774 1
775 3
776 -19
777 1
778 -7
779 -9
780 -3
781 -31
782 -11
783 5
784 -5
785 -5
786 -1
787 3
788 3
789 -9
790 -9
791 -9
792 -1
793 5
794 -13
795 -5
796 3
797 5
798 -19
799 5
800 3
801 -5
802 1
803 3
804 -11
805 1
806 -1
807 1
808 -9
809 -5
810 -1
811 5
812 -5
813 5
814 5
815 -11
816 5
817 -13
818 -11
819 3
820 5
821 -1
822 1
823 5
824 -9
825 5
826 1
827 -1
828 5
829 3
830 -9
831 5
832 -1
833 5
834 -1
835 -7
836 5
837 -7
838 3
839 1
840 -7
841 1
842 -7
843 5
844 1
845 3
846 3
847 1
848 5
849 -3
850 3
851 -5
852 -13
853 5
854 -15
855 1
856 3
857 -1
858 -19
859 -9
860 1
861 3
862 -3
863 5
864 -11
865 1
866 -1
867 5
868 5
869 1
870 5
871 -3
872 5
873 -15
874 3
875 -1
876 -7
877 5
878 5
879 5
880 5
881 5
882 1
883 -1
884 -19
885 3
886 -5
887 5
888 -3
889 -15
890 -1
891 -11
892 5
893 3
894 5
895 3
896 -7
897 5
898 -11
899 3
900 3
901 -1
902 -1
903 -15
904 -1
905 5
906 -5
907 -9
908 5
909 -3
910 -5
911 -27
912 3
913 3
914 5
915 5
916 5
917 5
918 -11
919 1
920 3
921 5
922 -5
923 -21
924 -3
925 -1
926 1
927 3
928 -3
929 3
930 5
931 -7
932 5
933 3
934 -7
935 -1
936 -1
937 -3
938 -7
939 5
940 -9
941 -3
942 5
943 -1
944 -13
945 -11
946 -1
947 5
948 5
949 3
950 5
951 3
952 5
953 -7
954 5
955 -15
956 1
957 1
958 -1
959 3
960 -7
961 3
962 -11
963 -17
964 3
965 5
966 -3
967 -7
968 1
969 5
970 -5
971 1
972 5
973 3
974 -1
975 3
976 5
977 1
978 -5
979 -3
980 -1
981 5
982 5
983 5
984 1
985 5
986 3
987 1
988 -3
989 3
990 -41
991 5
992 -3
993 1
994 5
995 5 NOTE that rows 114 to 1070 are "hidden."
996 1 Capability can be found under "Home, Format" above.
997 1
998 -5
999 3
1000 5

Winnings Risk Profile--Coin Flipping Game

< = -$20 < = -$15 < = -$10 < = -$5 < = 0 < = $5 2.1000000000000001E-2 3.5999999999999997E-2 0.06 0.14000000000000001 0.17199999999999999 0.57099999999999995

Winnings -- Upper Value of Classes ($)

Proportion

3.4.3

DISCRETE PROBABILITY DISTRIBUTION BASED ON HISTORICAL DATA --> Demonstrate use of Excel capability: =VLOOKUP
used when we have a discrete probability distribution to execute in a model
Issue: Maintenance policy -- new equipment (two motors, one always on standby if needed to be installed)
Problem: BusQues: What's the recommended maintenance policy?
Decisions: (a) Repair when failure occurs -- no scheduled maintenance. Can show in
(b) Establish a preventive scheduled maintenance to replace/overhaul motor. a picture
options: b1. after four days
b2. after five days
Objective Measure: Costs of breakdown and repair -- cost/day (Of course, want a low cost)
Constraints: Costs set for breakdown and for overhaul; breakdown distribution from history or from mfr. Picture of Days to next Breakdown
Data: Distribution of Motor Breakdown Breakdown: Replace/repair always completed prior to next day's production
A Discrete Probability Distribution - several values Costs If Breakdown
Day Breakdown Occurs Likelihood Replace $2,000
less than 4 0.00 Lost Prod $5,000
4 0.25 Repair $4,000
5 0.50 Total $11,000
6 0.25 Preventive: Replace/overhaul always occurs after hrs on overtime
7 or more 0.00 Costs No Breakdown NOTE the use of =VLOOKUP to choose NOTE: For example 1 on previous spreadsheet:
Total: 1.00 Replace* $3,000 *using overtime values from a random variable in this model. Could have used VLOOKUP with a cum prob table as shown here:
Lost Prod Will always use =VLOOKUP within a core model Prob Cum Prob Coin
Overhaul $3,000 to choose values from a discrete probability distrib. 0.50 0.00 Heads
Total $6,000 =VLOOKUP(value,cum prob table, column of table to choose) 0.50 0.50 Tails
NOTE: we need to construct a cum prob table. Result: Heads
Analysis: Build simulation models of machine operation with breakdowns and/or replacements.
Use models to evaluate each of the three possible maintenance policies.
CORE MODEL WITH NO SCHEDULED MAINTENANCE: CORE MODEL WITH SCHEDULED MAINTENANCE:
Time between Breakdowns Cost of Repair and Replace (using some input data from previous model)
INPUT DATA: Prob Cum Prob # Days Cost of Sched Overhaul DECISION:
NOTE: "Set up" the discrete prob distrib to use VLOOKUP 0.25 0.00 4 Cum Prob Preventive Maintenance Period (Days)
0.50 0.25 5 Distrib $11,000 AFTER 4
0.25 0.75 6 in bold $6,000
CORE Break -down Rand # Days to brkdwn Total Days Cost of R/R ($) Total R/R Cost ($) Next Event Rand # Days to brkdwn Event Total Days Cost of R/R ($) Total R/R Cost ($)
MODEL:
1 0.4580482498 5 5 $11,000 $11,000 1 0.9973564926 6 Sch Maint 4 $6,000 $6,000
Suppose we operate continuously for a quarter and then shut down for a week. So, we say let's have a core model of 18 breakdowns -- which is approximately 90 days. 2 0.5356485547 5 10 $11,000 $22,000 2 0.8648260696 6 Sch Maint 8 $6,000 $12,000
3 0.6721520938 5 15 $11,000 $33,000 3 0.0025891477 4 brkdown 12 $11,000 $23,000
4 0.5475774022 5 20 $11,000 $44,000 4 0.3630036941 5 Sch Maint 16 $6,000 $29,000
5 0.2937383155 5 25 $11,000 $55,000 5 0.4128297468 5 Sch Maint 20 $6,000 $35,000
6 0.8231604438 6 31 $11,000 $66,000 6 0.4978737094 5 Sch Maint 24 $6,000 $41,000
7 0.8490768412 6 37 $11,000 $77,000 7 0.3031078095 5 Sch Maint 28 $6,000 $47,000
8 0.1859596779 4 41 $11,000 $88,000 8 0.1149988264 4 brkdown 32 $11,000 $58,000
9 0.9429929231 6 47 $11,000 $99,000 9 0.4184209103 5 Sch Maint 36 $6,000 $64,000
10 0.5655454973 5 52 $11,000 $110,000 10 0.3303844014 5 Sch Maint 40 $6,000 $70,000
11 0.2539636244 5 57 $11,000 $121,000 11 0.4475751236 5 Sch Maint 44 $6,000 $76,000
12 0.1115642504 4 61 $11,000 $132,000 12 0.0758681563 4 brkdown 48 $11,000 $87,000
13 0.3260970706 5 66 $11,000 $143,000 13 0.0715107669 4 brkdown 52 $11,000 $98,000
14 0.3013785082 5 71 $11,000 $154,000 14 0.944493613 6 Sch Maint 56 $6,000 $104,000
15 0.1520123676 4 75 $11,000 $165,000 15 0.365604379 5 Sch Maint 60 $6,000 $110,000
16 0.7226853766 5 80 $11,000 $176,000 16 0.0443980306 4 brkdown 64 $11,000 $121,000
17 0.1717721507 4 84 $11,000 $187,000 17 0.9841667374 6 Sch Maint 68 $6,000 $127,000
18 0.0223291209 4 88 $11,000 $198,000 18 0.7020847587 5 Sch Maint 72 $6,000 $133,000
NOTE: Core Model should conform to how we operate. Cost per Day Cost per Day
If only during week, perhaps model one week. $2,250.00 Avg $1,847.22
If continuously, then something like this -- more days.
NOTE: Could have core model of 18 breakdowns or about 90 days -- as above.
Output: Average cost per day -- as shown here.
Replicate and record Cost Per Day each time.
Simulate these 18 breakdowns many times using Data Table -- e.g., 1,000 times. Then, simulate scheduled maintenance (four and five days).
OPTION: Could have core model being just one breakdown -- objective $/day --
since each breakdown results are independent of other breakdowns.
Then, simulate this breakdown many times with Data Table.
OPTION: Model one month and then use Data Table to simulate many months.
Thus, core model would stop after 30 days.
(If costs tracked and discussed in terms of months ~ 30 days.)
Output: A distribution of maintenance costs per month.
Avg of the 1,000 cost/day values, each calculated from 30 consecutive days
StDev of the 1,000 cost/day values, each calculated from 30 consecutive days
Summary TABLE OF RESULTS: Examined 30 consecutive breakdowns -- sample of 1,000 90 percentile of the 1,000 cost/day values, each calculated from 30 consecutive days
of Analysis OPTION AVG COST/DAY STDEV COST/DAY 90 PERCENTILE COST/DAY
Results: No Sched Maint $2,245
Sched Maint - four days $1,928
Sched Maint - five days $2,021
GRAPHS OF COST PER DAY (30 consecutive days) -- RISK PROFILES PERHAPS KEY OBSERVATIONS/INSIGHTS
Business Conclusions, Insights, Recommendations:
SIMULATION MODELING STEPS:
understand define build execute organize/interpret/answer business questions
"BUSINESS BUSINESS CORE REPLICATE 1,000 OR MORE TIMES RISK PROFILES
QUESTIONS" PROCESS MODEL(s) RECORD OBJ MEASURES SUMMARY MEASURES
LIKELIHOOD ESTIMATES
"ANSWERS"

Probability Distribution of Days to Next Breakdown (Discrete, derived from historical data)

4 5 6 4 5 6 0.25 0.5 0.25

Days to Next Breakdown

Probability

3.5.1

SLIGHTLY DIFFERENT SITUATION -- ADD VARIABLE REPAIR TIME Demonstrate the use of Excel's function: =NORMINV for a Normally distributed variable.
Issue: Maintenance policy -- new equipment (motors is weak link in 24-hour operation) Value Normal Line
Problem: Bus Ques: What is the recommended maintenance policy? 2.0 0.004
Decisions: (a) A1: Repair when failure occurs. Can show as a 2.5 0.018
(b) Establish a preventive schedule to replace/overhaul motor. picture. 3.0 0.054
options: B1. Overhaul after four days 3.5 0.130
B2. Overhaul after five days 4.0 0.242
Objective Measure: Minimize costs per day (or other time unit) of breakdown and repair. 4.5 0.352
Constraints: No other options Consider this change to example 2. 5.0 0.399
Data: Distribution of Motor Breakdown: Lost production and repair costs depend on repair time -- which is random. 5.5 0.352
time to next breakdown: Costs If Breakdown RANDOM REPAIR TIME -- CONTINUOUS DISTRIBUTION 6.0 0.242
Day Breakdown Occurs Likelihood Replace $2,000 Lost Production Time (repair/replace) THUS: 6.5 0.130
less than 4 0.00 Lost Prod $1000* Hrs NORMAL: mean = 5 hrs Cost of any breakdown = 7.0 0.054
4 0.25 Repair $800*Hrs stdev = 1 hrs $2000 + ($1000+800)* HRS (repair) 7.5 0.018
5 0.50 8.0 0.004
6 0.25 Preventive: Sched overhaul time is constant and thus lost production is constant.
7 or more 0.00 Costs No Breakdown
Total: 1.00 Replace $2,000 Normal Distributions
Lost Prod $2,000 Can use =NORMINV(CumPr,mu,sigma)
Overhaul $2,000 to find random values of a normal distribution if
Total $6,000 we know mu and sigma. For random cumulative
probability, we use the function =RAND().
Analysis: Build simulation model of machine operation with breakdowns and/or replacements. DEMO: 6.3 values from a normal, mu=5, sigma = 1
Use model to evaluate each of the three possible maintenance policies.
Core MODEL WITH NO SCHEDULED MAINTENANCE -- Six Breakdowns:*
Time between Breakdowns
Prob Cum Prob # Days Fixed Cost of R & R Lost Prodn cost/hr Repair Cost / hr Repair Time (hrs)
0.25 0.00 4 Normal Distrib
0.50 0.25 5 Mean: 5
0.25 0.75 6 $2,000 $1,000 $800 Stdev: 1
* change from example 2
Break -down Rand # To Next Brkdwn Total Days Rand # Rep/Repl Time (hrs)** Fixed Cost Lost Prod Cost Repair Cost TotCost of This R/R ($) Total R/R Cost ($)
1 0.8305 6 6 0.2291 4.26 $2,000 $4,258.21 $3,406.57 $9,665 $9,665
2 0.3287 5 11 0.4464 4.87 $2,000 $4,865.33 $3,892.27 $10,758 $20,422
3 0.0025 4 15 0.2152 4.21 $2,000 $4,211.48 $3,369.19 $9,581 $30,003
4 0.3061 5 20 0.6492 5.38 $2,000 $5,383.11 $4,306.49 $11,690 $41,693
5 0.5620 5 25 0.5435 5.11 $2,000 $5,109.29 $4,087.43 $11,197 $52,889
6 0.2790 5 30 0.3850 4.71 $2,000 $4,707.64 $3,766.11 $10,474 $63,363
Cost/day: $2,112.10
Core model of approximately one month.*
** NOTE: Will NOT use the same RAND() for a second random variable -- always a new value of RAND().
In this case, CORE model could be one breakdown -- if objective measure cost/day
since the results of one breakdown are NOT affected by the previous breakdown.
NOW, use Data Table to replicate many times --> many months of operation, say 1,000, recording the objective measure cost/day for each replication.
THEN, summarize the results by calculating characteristics of the risk profile like mean, stdev, percentiles, etc. of "Cost/day for six breakdowns"
Also, graph and display the "risk profile."
Business Concl, Insights, Rec:

Repair Time Distribution (Normal, mean=5 hr, stdev=1 hr)

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 4.4318484119380075E-3 1.752830049356854E-2 5.3990966513188063E-2 0.12951759566589174 0.24197072451914337 0.35206532676429952 0.3989422804014327 0.35206532676429952 0.24197072451914337 0.12951759566589174 5.3990966513188063E-2 1.752830049356854E-2 4.4318484119380075E-3

Repair Time (hrs)

Prob Function

3.6.1

Issue: Single Barber Shop (Common Model Type) DEMONSTRATE THE USE OF TWO CONTINUOUS PROBABILITY DISTRIBUTIONS AS INPUTS
Problem: BusQues Can we develop a better understanding of current operations? Uniform and Exponential Formulas -- and show Normal again.
Decisions: None to model. Understanding may lead to decisions to improve. x P(x)
Objective Measures: Average wait time of customers (in line waiting) and percent barber is idle (perhaps average total time of customers in shop.) 10 0
Constraints: Only one barber; FCFS, estimates of arrival and haircut time distributions 14.99 0
Data: Estimated time to cut hair -- Uniform distribution over the interval 15-25 minutes. DEMO: 15 0.1
NOTE: Can choose next service time with this formula: =min+range*RAND() =15 + (25-10)*RAND() 24.2 MIN 25 0.1
OR perhaps -- Normal distribution with mean = 20 minutes and stdev = 4 minutes x f(x)
NOTE: Can choose the next service time with this excel function: =NORMINV(RAND(),mean,stdev) 18.4 MIN 8 0.001
10 0.004
Estimated arrivals -- random with two customers arriving every hour ( one every 30 minutes) on average. 25.01 0 12 0.013
Thus, interarrival time can be modeled as an Exponential distribution with mean = 30 minutes. 30 0 14 0.032
NOTE: Can choose next inter arrival time with this formula: =-avg*LN(RAND()) = -30*LN(RAND()) 3.6 MIN 16 0.060
Analysis: (e.g., time to next arrival) 18 0.088
Operaton of barbershop for 10 consecutive customers -- typical of one day. 20 0.100
Core Model: LET'S BUILD IT! ONE DAY OF BARBERSHOP OPERATION LET'S USE ZERO, 0, AS THE TIME WE OPEN 22 0.088
Haircut Time: Uniform: Low: 15 High: 25 minutes 24 0.060
Normal: mean: 20 stdev: 4 minutes In a real case, only one would apply 26 0.032
Inter Arrival Time*: Exponen'l mean: 30 minutes 28 0.013
*time to next arrival 30 0.004
32 0.001
What occurs in the operation of a barbershop that we want to record? ---> to be able to calculate the objective measures (avg wait time, percent idle, avg total time)
ROWS: one for each customer -- to keep track of what happened to that customer and when
COLS: key occurences that happen for each customer and when
Customers Time to next arr x f(x)
0 0.033
1 10 0.024
2 20 0.017
3 30 0.012
4 40 0.009
5 50 0.006
6 60 0.005
7 70 0.003
8 80 0.002
9 90 0.002
10
*time to the next arrival
or, time between arrivals

Haircut Time Distribution (Uniform from 15-25 min)

10 14.99 15 25 25.01 30 0 0 0.1 0.1 0 0

Hair Cut Time (min)

Prob Function

Interarrival* Time Distribution (Exponential, mean=30 min)

0 10 20 30 40 50 60 70 80 90 3.3333333 333333333E-2 2.388437701912631E-2 1.7113903967753068E-2 1.2262648039048078E-2 8.7865712705242262E-3 6.2958534279187279E-3 4.5111761078870903E-3 3.2323989288135018E-3 2.3161150407600513E-3 1.6595689455954647E-3

Time to Next Customer (min)

Probability Function

Haircut Time Distribution (Normal, mean=20, stdev=4 min)

8 10 12 14 16 18 20 22 24 26 28 30 32 1.1079621029845019E-3 4.3820751233921351E-3 1.3497741628297016E-2 3.2379398916472936E-2 6.0492681129785841E-2 8.8016331691074881E-2 9.9735570100358176E-2 8.8016331691074881E-2 6.0492681129785841E-2 3.2379398916472936E-2 1.3497741628297016E-2 4.3820751233921351E-3 1.1079621029845019E-3

Hair Cut Time (min)

Probability Function

3.6.3

Possible Objective Measures
Core Model here -- 10 customers ALL TIMES IN MINUTES Usually, some, not all, of these objective measures
Expon Inter Arr Time Time Haircut Begins Uniform Haircut Time Time Haircut Ends Time in Barber Shop Barber Idle Avg Wait Time Avg Time in Shop Normal Haircut Time
"Typical 10-4 shift" Time of Arriv Time Waiting 12.1 min 32.8 min
Customer StDev Wait Time StDev of Time in Shop
1 34.5 34.5 34.5 16.0 59.0 0.0 24.6 34.5 12.1 min 14.6 min 24.6
2 6.6 41.0 59.0 21.4 81.9 18.0 40.9 0.0 90th Percentile Wait Time 90th Percentile of Time in Shop 22.9
3 28.7 69.8 81.9 22.1 95.4 12.1 25.7 0.0 22.2 min 43.4 min 13.5
4 83.3 153.0 153.0 18.6 169.3 0.0 16.3 57.6 Max wait time 16.3
5 51.2 204.3 204.3 24.9 223.7 0.0 19.4 34.9 35.7 Barber Idle Time - % 19.4
6 1.3 205.6 223.7 24.1 241.9 18.1 36.3 0.0 40% 18.2
7 48.7 254.3 254.3 23.2 277.0 0.0 22.7 12.4 Assumptions: 22.7
8 2.0 256.3 277.0 23.6 296.4 20.7 40.1 0.0 FCFS 19.4
9 23.8 280.0 296.4 23.0 316.2 16.3 36.2 0.0 customers arrival times are independent 19.8
10 0.4 280.5 316.2 17.3 346.6 35.7 66.2 0.0 Assume no balking if arrivals see large wait line. 30.4
Could build a core model of 6 hours (360 minutes) More complicated -- need to stop model when total time is 480 minutes -- similar to Ex 1. blue cell a column of gray cells
Model one day (=6*60=360 minutes). Then, use Data Table to replicate 1,000 days 360 go
Have a large number of rows
NOTE: Cannot just have core model of one customer --> results of one are NOT independent of previous customers. Assume no balking if arrivals see large wait line.
Now, replicate the Core Model 1,000 times -- use Data Table recording each time (for example) Avg Wait Time, 90 Percentile Wait Time, and Idle Percent
Results. Organize results of this sampling of 1,000 "Barbershop Operations for 10 Customers"
For example, sample mean and stdev of each measure. Also, graphs (risk profiles) of the distribution of each measure.
Specific "answers" to business questions: Estimate of Avg Wait of customers -- use mean of 1,000 avg wait times.
Estimate of High Avg Wait that is exceeded about 10 percent of time -- use 90 Percentile of the 1,000 avg wait times.
Estimate of 90 Percentile of Wait Time -- use mean of 1,000 90 Percentile Times.
Estimate of Low 90 Percenttile of Wait time that is exceeded 90 percent of the time -- use 10 Percentile of the 1,000 90 Percentile times.
Estimate of Idle Percent -- use mean of 1,000 idle percents
Estimate of Idle percent that is exceeded about 25 percent of the time -- use 75 Percentile of the 1,000 idle percents.
NOTE: All these estimates are for the barbershop operations for 10 customers.
Business Conclusions (Insights and perhaps recommendations)
Construct in everyday language the understanding of the barbershop operations with a focus on "answers" to
the Problem Definition (step 2) above. Use statements and perhaps refer to tables and graphs.
Example of Replications: -- use Data Table
Shop Opns -- 10 Cust -- Uniform Time References back to core model Shop Opns -- 10 Cust -- Uniform Time
Avg Wait (min) 90 Percentile Wait (min) Avg Shop Time (min) Percent Idle Example Summary Table Avg Wait (min) 90 Percentile Wait (min) Avg Shop Time (min) Percent Idle
12.1 22.2 32.8 40% Barbershop Serving 10 Customers What if MGR also asked for 12.1 22.2 32.8 40% Barbershop Serving 10 Customers
1 13.8016199692 26.1695956325 34.3035148475 0.2586820954 Summary of Estimated Results Table: 90 Percentile of Avg Wait 1 43.323475672 61.9723776823 62.6464477854 0.0060016661 Summary of Results Table:
2 7.0337251172 19.2281691672 27.5143345501 0.5378828114 Avg Wait Time (min) = 11.3 23.7 2 1.6545969677 4.4745910262 22.0890406416 0.6711312808 Avg Wait Time (min) = 11.6
3 4.8809097177 12.3393823673 25.1330849299 0.3612920681 90 Percentile of Wait Time (min) = 26.0 (to see how bad it might be) 3 15.9288959096 34.9869642173 37.6679007486 0.3023561194 90 Percentile of Wait Time (min) = 26.3
4 8.3029578266 27.9375579394 29.9962675859 0.4794705244 Avg Time in Shop (min) = 31.3 4 13.5849064231 27.3874457748 34.9972069633 0.3937869923 Avg Time in Shop (min) = 31.6
5 8.4636877091 25.5826020619 27.0838480767 0.4531114875 Percent Time Barber Idle = 38% 5 8.6538684853 18.4862133282 28.1868103037 0.0417768706 Percent Time Barber Idle = 37%
6 13.6220451464 38.5795317002 34.6531296913 0.0431767646 6 2.8895562753 8.9494782491 23.4167705215 0.593587956
7 15.520653396 34.4555662869 35.2679001673 0.262102008 What if wanted the stdev of avg wait time? -- to show variability of this measure. 7 5.9923871248 21.100782324 26.194687283 0.3108066684
8 29.0388766809 51.0964525052 48.5663252013 0.0650872613 StDev of Avg Wait Time (min) = 9.0 8 14.5902202434 31.2658154177 34.2407336338 0.0707050975 StDev of Avg Wait Time (min) = 9.8
9 11.759001969 33.6029366477 32.6139146813 0.5133672106 9 1.9461366823 1.9461366823 20.8935050964 0.56376176
10 4.6668501134 12.9256212154 23.2447649464 0.4513763268 What if wanted to show Risk Profile of Avg Wait Time? -- To show variability 10 10.2482363895 20.0109962218 29.6526027753 0.1905482236
11 30.7791834848 76.3782478883 50.9144694002 0.3099669908 Labels Class Freq Propor 11 32.9171099304 58.073817706 51.4371650992 0.0445439571
12 3.0289749529 11.0721374066 22.4245703451 0.440373177 0-5 5 565 0.57 Use =FREQUENCY 12 36.5185938136 73.1703387253 56.0031219886 0.0872266146
13 5.8479074027 21.5029612731 24.0785937264 0.2712652852 >5-10 10 180 0.18 13 16.1581481953 39.4194810844 36.6769155658 0.3921633254
14 11.8571781031 24.4850138022 32.3778342867 0.2389109082 >10-15 15 116 0.12 14 42.883629865 70.7413681899 64.1056492705 0.0638843145
15 10.5372255675 22.3364916064 31.1157701258 0.3452189111 >15-20 20 50 0.05 15 32.9451594442 50.5609433682 53.7369262427 0.1320939206
16 16.7747753382 33.9918580121 37.51249975 0.2104601312 >20-25 25 42 0.04 16 0.7347143735 3.462260131 19.9110924368 0.5707544839
17 10.2057923357 23.9734092312 28.7579543096 0.4868286616 >25-30 30 21 0.02 17 1.9642076962 4.9013016996 21.6619867266 0.60971691
18 0.2181372363 0.2181372363 19.4302415544 0.4883953896 >30-35 35 11 0.01 18 11.4201446806 35.6784716279 30.678519792 0.2854135947
19 1.8088572673 6.5907079776 21.8512090607 0.5032426156 >35-40 40 15 0.02 19 9.3404431393 25.5561778842 30.519876293 0.3835058202
20 9.1633801902 19.7339187218 29.5308045374 0.2489904812 >40 >40 0 0.00 20 2.0148986129 6.5011095048 22.00272969 0.5139735466
21 9.8364129642 19.0358953192 30.9185888671 0.2899030726 total 1000 1.00 21 4.0813685909 13.6576846797 22.8242350696 0.5121940366
22 21.9874353036 37.771031806 42.4070433297 0.0702424632 Use =FREQUENCY 22 11.5006242752 28.1871564933 32.5771373133 0.2266303396
23 9.3232382999 21.6708368486 29.9021050291 0.53813073 23 6.1033403782 13.6170375895 25.896845452 0.3099583794
24 3.899160299 14.3585320822 24.021576653 0.3481561376 Use Insert, Chart,… 24 13.1738606677 24.4867432517 31.7346499997 0.5177796955
25 3.2607955211 9.9534324942 22.3949952674 0.2034548835 25 22.2517799216 45.8130283248 43.2341987586 0.2146121882
26 6.2013716307 19.4513813978 25.644290907 0.4419228589 26 7.9693673218 20.1553746576 29.3998470357 0.1120914233
27 6.4781269723 14.6505494619 25.7997449876 0.5706268404 27 12.5141256826 27.3143609543 32.573021252 0.3698778962
28 18.4860210917 50.657074658 38.7201933857 0.4062158554 28 1.7676186916 6.0480867447 20.8244805156 0.5894160983
29 13.5405470056 40.1170032238 34.7711501206 0.1918189046 29 16.851231435 48.2193672506 38.1075755845 0.3187822645
30 16.8465647481 41.1794198137 37.800729793 0.2122820715 30 2.329983463 8.4461650507 22.1393987095 0.2519010012
31 5.9690172151 18.7784367448 24.6452949922 0.4213668877 31 29.8857666545 69.0040589729 49.7244096823 0.3096381548
32 13.7709611135 28.4311522115 32.7427111378 0.4346881899 32 3.1200734563 11.0643013738 23.6265986977 0.557603354
33 15.9192889114 46.1173629316 37.3526304034 0.4083371356 33 8.2298703635 17.8381220649 27.6576038484 0.3915657714
34 1.9244266573 1.9244266573 21.1297871765 0.6791948611 34 5.8013860441 17.0341493638 24.5330408237 0.5331013054
35 8.7642637951 22.2690263862 28.6953645363 0.1415229618 35 34.4124218218 69.065445418 54.7406338554 0.2553107205
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37 2.2498301923 7.4524394216 22.6619788596 0.4068746732 37 23.173480644 50.4279320798 42.8310460291 0.4942809557
38 5.8227931464 21.4287512399 25.2508426288 0.5896023409 38 6.4709126808 22.0448217924 26.3928407092 0.3668286223
39 4.5655774028 11.3672505174 22.9656892455 0.169914375 39 6.2980129192 16.7603817811 27.115828589 0.2225921985
40 9.3076449281 19.6039961338 29.9487707701 0.2662997098 40 5.1216192607 14.2266300877 25.3151967426 0.492321213
41 27.2499616461 48.019286918 47.1855707477 0.2408487529 41 21.2492289098 54.841358143 41.6033413829 0.2490170586
42 9.7369778727 24.1708308647 30.3371345649 0.2721929406 42 9.6411296741 17.121238444 28.5165237225 0.2495773409
43 9.687006685 19.5455907549 29.1092111053 0.3779124893 43 9.6837465565 28.5160525068 29.9444988129 0.5727681351
44 3.6310037066 15.0210103716 22.5026385471 0.643667098 44 7.6557587276 14.82903509 28.1412651593 0.170344463
45 8.9973228725 27.432891086 27.6441490087 0.4607348623 45 1.6814725267 4.0827673398 21.5842874804 0.5900793879
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47 3.3149381171 9.2501155458 24.776964966 0.5081876822 47 17.4517504092 35.8243999517 37.1442231274 0.1256048639
48 4.1322742644 15.7526626486 24.0478931749 0.4801920161 48 7.2154195665 20.5217867302 27.543594716 0.4612859381
49 11.1057416238 27.2188339002 30.9864452188 0.5326659753 49 16.2875009431 45.0347270761 36.7485981741 0.2632278152
50 7.6235978566 16.304013514 28.8690011715 0.4336001021 50 1.6842024621 4.6962006189 21.8675075568 0.604257067
51 7.389820248 17.4344293058 27.8037750572 0.557494891 51 8.5743559616 19.8876878857 29.9282534966 0.5092476399
52 11.4620978178 34.8176804818 31.4941668888 0.38617975 52 45.6822309955 69.1824576519 66.2247219264 0.1000768493
53 9.4405011873 31.0577892477 30.0166426235 0.4364277418 53 0 0 19.2914937293 0.6218153175
54 31.1434724873 52.3696787978 49.6495507178 0.1028110785 54 4.1455154544 12.509111875 22.8015253622 0.6419521622
55 22.2314132992 47.2769680625 42.6994663484 0.1365052068 55 3.7100073026 10.7605808499 24.9741077545 0.4938645413
56 17.8027900898 40.098648192 37.2751009456 0.2815258126 56 4.7113058232 17.9553754328 25.6691334648 0.4741541609
57 16.5318385789 45.1254403618 38.4610230599 0.4845930819 57 3.7993394623 11.6907139981 22.735159809 0.5337262253
58 20.3678925533 53.9993429749 41.8692047982 0.3781588709 58 11.7260336485 25.7321283059 31.4139713933 0.0914589257
59 1.2974779641 4.407435685 19.6106994738 0.7019943394 59 6.6890118417 16.2395415468 27.2165389486 0.3517053558
60 2.6141070435 7.333227275 23.2236112674 0.3525593462 60 5.8896278477 15.3959349795 25.6407828625 0.4932290787
61 7.299969287 16.715176423 26.1947441413 0.3544767899 61 8.03564543 22.6264877821 28.437099682 0.3247120964
62 17.1696566387 38.695702499 37.1034540615 0.3569186365 62 33.1094499122 72.6129622129 51.7544562959 0.1927842236
63 5.5083777414 15.8823221436 25.2003296778 0.4650596418 63 13.6889169992 22.4636114184 32.0812636016 0.176543581
64 21.6240432043 48.4709838996 41.5231690078 0.4470562152 64 5.3546167817 12.6539220121 25.3985921151 0.3021604849
65 5.3255773693 17.7656671703 24.4605820739 0.7075351093 65 8.2779028551 22.5731266141 28.125118356 0.4301572153
66 18.080526535 37.3616340338 38.7686958454 0.2099647224 66 4.4884876452 16.4337855379 24.9931664408 0.6449657364
67 6.1351666626 14.1927962043 24.27092469 0.4272076616 67 14.487658697 25.3977207489 35.6105005518 0.0682166894
68 29.1841988927 51.1611231133 49.3793856931 0.2062093101 68 19.0178764869 46.3360831176 36.1644718026 0.3280151549
69 6.564982317 20.3843437273 25.7626336773 0.6084316093 69 10.6145314653 27.0181467135 32.2703683824 0.0673008293
70 6.0731943973 16.3712459689 26.0998050182 0.4945886416 70 7.5028085323 17.5641542932 26.9514040092 0.338985491
71 1.0125478668 3.8703149537 20.5963414455 0.5201278044 71 14.4070172065 33.4154915183 33.8918988589 0.5691764946
72 6.6470570018 20.7149699214 28.7361765998 0.3143465981 72 10.7776432834 23.0029843151 29.9458249681 0.3074717689
73 6.7188504359 15.4170452264 27.4235078564 0.2762003214 73 20.1283179 45.0597259726 41.4198915514 0.2210407382
74 17.8050563409 37.5278337212 36.834952024 0.1024145457 74 5.6013246216 13.3286452835 24.4766524843 0.5428344049
75 5.4258380891 12.2073600732 24.3744104845 0.5568403622 75 8.8803998386 27.5420198107 29.8212390515 0.5629891299
76 26.3955300136 62.4981429006 47.6779874311 0.4384998419 76 8.8977046742 21.2185879458 27.837916766 0.4718991682
77 17.8635504077 34.5419036483 38.2106054744 0.1470619503 77 4.0327987179 11.8233362823 23.2313200018 0.5405324614
78 3.1246186924 8.3054367897 23.842722281 0.5438879074 78 14.7334994292 33.1609905766 32.0595454418 0.4905045262
79 13.3082115122 34.1154434834 34.0761187757 0.168537892 79 4.9355166549 14.729594823 25.9284772904 0.4039960448
80 15.0838245153 36.5399966056 35.3888411186 0.3089635782 80 1.1069620211 1.1069620211 20.8309762883 0.627716824
81 2.1240229116 5.6759317494 22.5889120905 0.5297022353 81 11.944496943 33.6219663613 32.8257289603 0.2609002779
82 8.7042553413 20.0803659157 30.4550030611 0.2455226248 82 6.1251205701 16.0144774039 25.590437949 0.4001557029
83 11.6292595155 32.9805089577 30.9390568248 0.467865481 83 13.1099052517 25.4431326327 34.5597279909 0.308371946
84 5.6799956851 18.006622946 26.3747007677 0.5157193742 84 1.6434559421 2.9905024826 20.3285683189 0.5237676353
85 24.7775401121 44.8625082835 45.6519944702 0.1985330769 85 15.7832513389 26.4690221019 37.0958538455 0.114257453
86 14.4154781515 39.2051900652 35.2663686042 0.4734998708 86 13.8943687367 27.1358412864 33.7165745282 0.2692242001
87 5.0275366374 17.3877186925 26.2308305709 0.5639847909 87 20.6464896876 31.9647850177 40.9256339122 0.2465794615
88 6.2182241638 15.8953326628 25.209629441 0.5846967502 88 6.3594685108 14.6919108165 26.1948215421 0.3165499185
89 23.8178618333 42.9104747381 45.0129951366 0.1306837532 89 18.7694329304 37.528810058 38.8803679167 0.3183281842
90 2.2913142009 10.0142554297 23.6928773019 0.3499583326 90 29.6816132394 64.729761202 50.9283639132 0.3015439792
91 16.0901619721 33.8412541257 35.1782087779 0.2498406897 91 6.1225785936 18.1042368256 24.1768071152 0.4850749213
92 26.2597614751 51.5655922388 47.0633690766 0.3318681092 92 6.6855694358 22.3104247909 26.5520731698 0.2790740815
93 5.1619944801 14.8279321359 24.6774574129 0.3811068868 93 9.7954492359 21.9134888087 31.4505965207 0.3786504097
94 17.7978070431 30.444886723 38.9989794198 0.2444340266 94 44.9204541978 67.5255939155 63.9947818792 0.2763726087
95 1.6590950236 1.6590950236 22.6787045598 0.7283572417 95 5.9577221924 18.0540994846 25.627512129 0.3296657311
96 5.8461658817 16.1496018515 26.9227362041 0.4499525005 96 14.0812532254 34.9506077189 33.8840209709 0.0998287432
97 22.3543265743 40.0677490725 43.5338470055 0.148516494 97 11.6505783886 26.1812040446 32.9075724249 0.3266870667
98 17.9831373084 39.149402402 37.3566040598 0.4334733532 98 2.7599159786 8.7415155207 22.6073988428 0.5577631464
99 7.4798250836 19.6542457868 28.2498308182 0.4514168633 99 7.5072194937 18.0926176109 26.8578969608 0.3218236068
100 5.9829211633 13.3246944973 26.5286487452 0.4414127704 100 30.2994337235 47.4279298994 49.3045941089 0.1331324436
101 16.0931563468 42.0040385535 36.7016413873 0.3553481621 101 5.8715922726 23.6138622705 25.771946492 0.5782331692
102 16.7687755273 42.2474977625 36.4638654979 0.1691315901 102 10.8643819174 25.1440884041 29.7947694488 0.4842534405
103 11.6973701739 24.3388061911 31.0361800711 0.5308337471 103 8.7206625405 19.7214688949 30.3943490146 0.3374105752
104 32.5255335193 69.2327504619 53.2607929537 0.2458307173 104 12.9565025955 33.4249661242 31.8487190159 0.5976906105
105 3.7857147468 11.5143013566 25.4856074773 0.3445890576 105 5.7498580301 18.0726876784 25.8325302904 0.456498986
106 11.1946560317 33.3898717754 29.5926943283 0.171492974 106 5.7077036391 15.6527826 24.8701233736 0.5186548897
107 8.3548461264 19.6502991658 28.6489587234 0.3281331072 107 8.0102539686 19.4153593066 27.9290454158 0.2692717012
108 6.0402615894 16.4675149119 25.4612833935 0.5047089929 108 29.4974584146 52.3299990946 50.1425914148 0.1594278795
109 15.2213346267 33.5813944255 34.5209310274 0.2274563286 109 9.2980682536 16.5800233341 28.7152434868 0.1855164091
110 6.7344217627 17.1137320199 26.4572881517 0.3210042326 110 20.1773409734 45.9247931635 40.6560810724 0.0914622608
111 16.6396149023 30.3486724835 37.5346678514 0.315882216 111 10.9557994947 24.7622855338 31.2402005214 0.3117568783
112 6.4944174477 19.9839575397 26.8290038019 0.3594944561 112 20.9986474628 50.6231927951 41.055744566 0.2714948342
113 5.3109463214 18.4647078543 26.0652511665 0.3530756919 113 13.9178140373 26.6822771699 33.2926779137 0.18408875
114 7.1078700308 17.0463826372 26.0679726581 0.5624969837 114 8.8881535213 21.1982595133 28.7253702553 0.50625115
115 23.7175160624 44.3925637904 44.023599228 0.0952537599 115 8.4978049614 23.4053880162 28.3896776657 0.159827505
116 8.6266914468 28.271829477 27.9123773508 0.389606063 116 7.18512433 14.1482644526 26.0871302549 0.3912637037
117 10.1743543492 32.4970691615 29.8171347123 0.2187462066 117 3.4270784352 8.87718697 22.2806545268 0.5407861578
118 7.0016256187 23.6643044694 27.510420677 0.4837717197 118 2.6648571052 6.4670376472 23.0053162476 0.5381753129
119 9.4392321889 20.0806838237 28.2442285524 0.5141483971 119 13.5560265813 26.4151691723 33.8834784607 0.3088836359
120 7.5301770051 17.269952897 27.2097065444 0.2638614791 120 10.2048127348 30.0567066789 30.7024748738 0.3621291067
121 20.2848535007 44.8463840508 39.9372826387 0.386112153 121 13.8293670663 29.7485179079 35.6587326616 0.2576283595
122 7.9256580072 19.417891811 26.2481108454 0.3112535936 122 3.7874853172 10.5075430608 24.6936204577 0.3523209663
123 10.9279968328 24.9266420709 31.5801418947 0.1787130014 123 25.1935995194 56.5978266496 45.1646813441 0.1135357449
124 27.1254056032 65.2128802387 48.8287481419 0.2330789781 124 10.434083019 29.1562337834 30.4431961423 0.4547519226
125 5.7291382887 14.4673254255 26.201783234 0.3434332214 125 26.8327318502 44.2699275554 45.8941398934 0.0120535337
126 19.7773860613 38.4972731853 39.2822034481 0.2399212767 126 3.4383621646 10.474558438 24.0873066797 0.2209443711
127 8.6690799825 20.3305103115 29.0140184207 0.3327701997 127 10.3530630205 25.1875798324 31.6990968674 0.4016093748
128 14.5383286498 34.2974613107 33.9449638087 0.5267347002 128 9.8189874496 30.3739893875 30.1401627721 0.493088573
129 12.9287540526 36.2665363543 33.2263879555 0.3681497896 129 10.2413457925 29.6627829395 28.7920275682 0.3868896177
130 13.9608732268 43.3691222456 32.1683667419 0.5338729096 130 5.5286116869 14.9817231167 24.6131271924 0.5152395053
131 22.2206799706 42.9798905149 41.6592707596 0.0100003809 131 11.5038717122 23.5044435741 31.6267751718 0.4167756528
132 7.3071158032 18.7624676399 28.506265673 0.332189204 132 1.8132617071 7.6155480219 22.9289171865 0.2178454042
133 8.4522440965 15.9980803709 27.3406868021 0.4758444504 133 2.5891584225 9.7828637367 21.3112872803 0.5650417807
134 10.5906316865 18.8488762012 30.3491264927 0.2786080869 134 15.2353529492 36.6262116717 34.3453987472 0.378283235
135 12.670327608 35.5920326182 32.8204330205 0.3215467209 135 2.3320528402 6.0509271687 22.15571942 0.4149248214
136 4.8518011275 13.7997595983 24.0908784322 0.4483112948 136 2.0792612695 7.7369301052 21.9587079801 0.4940053363
137 13.2467686803 35.2465421626 32.6096418804 0.3439410175 137 12.2724738201 24.4489470201 32.3328361206 0.0532131956
138 4.0864446031 13.6849612647 24.7491024058 0.3788002374 138 5.4267061795 13.803230588 23.1787084799 0.3388523667
139 17.93405044 37.1063838415 36.9548035705 0.0973965159 139 4.0589621388 10.5848204586 24.7118558821 0.2841307749
140 21.258908676 57.8430738323 42.3555395884 0.3732430444 140 3.9122981606 8.5964879556 23.5934722143 0.322357202
141 37.8185100392 72.4578244252 56.8808652471 0.200739215 141 6.5262385534 15.7949805319 26.6100818713 0.2686920419
142 12.1721539408 24.6974768388 31.8022528875 0.3400308309 142 5.3749315294 17.2734339353 23.9048464501 0.5526101451
143 5.2555318382 17.8813406651 25.0697715834 0.4835189896 143 11.2691190794 29.700822121 33.5684322476 0.2146505507
144 4.1365135491 11.6928874146 23.2150359035 0.4169658727 144 6.8675868175 20.6755225037 26.564738191 0.486391523
145 5.2187487979 17.5261445814 26.67364811 0.452707019 145 7.238658744 24.5403833065 29.5581746888 0.3439089297
146 35.7415017701 60.2102040222 55.8102779111 0.0831837515 146 6.7823248521 18.7210827643 25.8678716735 0.3693538097
147 18.6245970119 36.8465081714 38.6466941313 0.0070233577 147 2.7584865814 9.0204472479 23.9448179662 0.2752120665
148 11.6554759318 29.8447011965 33.0532930918 0.3266844201 148 2.7825078796 7.5153032111 23.0639405884 0.42706047
149 18.4473579253 45.2198197805 37.210064246 0.4401214883 149 9.6103761116 22.3052075206 29.4836977307 0.3239941894
150 6.2442169803 19.527621464 25.4945502984 0.4778808988 150 8.4835314232 25.4714497258 27.8962751603 0.5423089808
151 11.599965635 23.2233910293 31.5958150603 0.2299910813 151 4.2803436924 15.5260668898 24.9183251391 0.4746781617
152 26.6211762349 42.1003250213 48.068450984 0.0378527769 152 5.0242504483 18.156342665 24.088631193 0.2696649473
153 9.7764745221 20.9869756709 29.9923990941 0.5668724646 153 8.2005244101 23.47073534 27.7513682629 0.380016729
154 3.632717781 17.0866287735 26.797015986 0.5316654851 154 2.3507188975 6.4826348849 20.5823960463 0.4851715345
155 26.3687229159 42.153980784 47.1424597165 0.1254501995 155 38.0091165711 62.5268395096 58.0807739471 0.1938710362
156 14.5614931631 34.235111076 34.3254077435 0.3339680635 156 6.344484658 19.5107528955 26.0359542608 0.5756439155
157 2.2673525336 5.6286300566 21.3360722461 0.6364911934 157 2.7793334325 9.7496398789 21.283377614 0.5662660647
158 7.3903310514 21.7948182017 27.9044084628 0.5419030456 158 2.1674600638 3.9935690588 20.4905115744 0.4386979652
159 9.2330459357 18.5525036881 27.6879541061 0.5102949715 159 39.7582089571 60.9914332641 59.2118689423 0.0190434757
160 4.4994833388 12.2155715369 25.0715532651 0.4176210872 160 12.8069259747 32.8346762068 32.727146253 0.5272662275
161 14.0757170504 27.199013432 34.1221395862 0.3201263434 161 12.3455091994 25.278173758 33.2305850386 0.4705705085
162 0.4591540771 0.4591540771 20.7408084841 0.5180726569 162 4.9277589227 12.224339325 24.8108497821 0.5036514529
163 15.7931086159 26.8796819015 35.685300735 0.1170520095 163 4.615308299 12.0433638244 24.9299057488 0.5510453878
164 13.627836335 30.7998352143 33.7490207536 0.095894368 164 11.4045082296 37.6693419135 30.1711923494 0.5270884979
165 9.7023349932 21.9598140166 28.9410895998 0.489247155 165 1.1251557974 1.1251557974 21.5287050076 0.5422534193
166 13.0085111647 29.4805922861 31.8312745455 0.2300107221 166 26.7554454981 45.2792908512 47.1833580979 0.3222681009
167 13.6504185167 43.3309933663 33.546067131 0.2729678618 167 26.1917765209 42.7307468106 46.3158753416 0.1412533291
168 16.579491439 46.5369669596 37.3834552574 0.1584436962 168 0.5564289119 0.5564289119 19.8216352224 0.5926803889
169 2.2734691962 4.5504939816 20.9413427652 0.4062310572 169 9.119773538 22.0561118009 29.0353277437 0.5238942448
170 12.4974791411 33.6260671852 31.4481641821 0.5519720821 170 3.7676495842 8.6304716852 22.4604619749 0.5492778195
171 2.3844796677 10.7756634711 22.1271864816 0.6563895071 171 36.3195923951 70.2723568621 58.5914156414 0.0882690793
172 9.4809939524 24.2816098519 29.4106205767 0.3880001747 172 14.414060389 40.8012109725 36.0062063056 0.5491254612
173 1.4953361871 2.2750775905 21.5481978516 0.2831619305 173 10.6688812368 35.8665901803 29.9375275133 0.6580587556
174 12.2386604123 28.8130468538 31.7448790058 0.505777691 174 2.4877047168 5.8995329814 20.7872405434 0.5992392225
175 2.19722349 7.696551868 21.8137986653 0.5691399264 175 3.6671896641 12.3055347702 25.5219690936 0.6349344676
176 26.2985131211 49.1001334611 45.851162061 0.1629180824 176 5.3058662547 15.5653466555 25.3581561846 0.2619070635
177 12.8618655456 30.6365659528 32.9288471571 0.4133486653 177 24.1317515449 44.2087130162 43.8590020884 0.233801876
178 6.3815283131 18.7770594963 28.0459735802 0.2951768358 178 15.5418092403 34.0448885141 35.8885001793 0.3524779869
179 9.553776407 24.0698177207 29.3501822633 0.48978534 179 22.4366002541 44.4233717605 43.4406466413 0.3074748749
180 10.126861075 24.0490850832 29.2563024986 0.549011934 180 6.5894939293 21.1382131861 28.1054145008 0.4258241494
181 2.1231722037 8.1902410067 20.9087572423 0.655097738 181 7.1427319808 19.4758911781 28.7483592793 0.2575422577
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183 10.1317081406 18.2090975293 29.4009207416 0.2840703343 183 29.1949730879 54.9128730042 48.997725126 0.1280509762
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210 19.8474853108 42.1867060188 41.1872833906 0.2294661494 210 6.9652808743 21.2229111599 27.6022434633 0.4524331238
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217 2.9902339472 10.2203670438 22.9057839281 0.4840783363 217 7.4703473728 20.3589909506 28.431335508 0.5489217231
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219 6.4875257943 19.0053954742 26.6201204816 0.5813650318 219 3.2773789039 8.7605404153 22.882605499 0.5965031491
220 47.4969322712 68.6345125101 67.6403764657 0.0876271227 220 11.129814126 22.4683010351 32.345047564 0.0351749041
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222 29.3391056571 57.9627946494 49.4318137363 0.1813755651 222 10.3785407401 22.3872976136 30.9670055695 0.3657351159
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224 5.954597856 17.6159684326 26.7538744052 0.540277712 224 6.6763049089 20.0240464334 26.3954291149 0.5737782982
225 20.5563681402 40.166628456 42.6504690675 0.1244001154 225 8.8619236599 23.4041737672 28.766749907 0.3202909742
226 26.2628263645 55.9568196332 47.6613194973 0.1870318129 226 14.7843511328 41.6068367501 35.1047175788 0.485536218
227 19.2485615931 49.1672507683 37.3698569687 0.5790446378 227 10.8238065463 26.6018606555 31.0572114084 0.4173371178
228 20.0106114277 35.1685515589 40.870974273 0.0552108532 228 6.3966331653 18.9115246888 25.9711879882 0.1595760626
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233 19.4085392922 42.4602458908 40.1758524182 0.5752150731 233 6.6687488371 19.8043403333 24.896285084 0.4911314457
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237 5.709688828 16.2813388709 26.2535604954 0.4407332594 237 16.1870680681 32.8937997039 36.6154225313 0.3648160132
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239 16.0668724336 37.3147494566 35.4957165288 0.3040774307 239 8.7279258491 29.2144159836 29.1800220244 0.5792705618
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244 8.4602944579 22.6173308801 28.286062312 0.4841152976 244 24.4498094656 51.8126561358 44.2996194879 0.2154926944
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249 10.5379009272 23.4901030738 29.1866000836 0.4086480927 249 7.1777948532 26.8173633324 26.4768645132 0.5366897058
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252 5.3581708385 13.4598675649 24.1256618569 0.3116164925 252 6.0980234271 16.7361949123 25.4033031178 0.2627723633
253 25.3381834939 68.7991786171 43.7769002252 0.2989897462 253 13.9806758998 34.3826108779 34.188788039 0.5510377477
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257 15.7639893825 38.3080390167 35.8951974784 0.4655473672 257 7.7926073503 23.2217664927 28.0300358774 0.4364907431
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259 7.192602774 18.2000111314 26.09367765 0.4286392683 259 4.2138986653 10.65141186 26.0008301002 0.3616784522
260 17.990583418 33.6388363792 36.6415383426 0.1510704378 260 20.8122359564 47.7820173756 40.8308548041 0.5157414789
261 10.7962056469 32.3134580807 30.9384754989 0.2143334468 261 12.1892532891 24.3924781712 32.3461766081 0.2294548355
262 6.3691769792 13.9516855229 24.6688770534 0.2900590883 262 9.4341272789 25.2541189184 28.8311689053 0.3707262438
263 10.004612904 33.7063037159 30.483403465 0.354470172 263 4.7762190297 17.2385410287 25.7062791093 0.5059675084
264 25.156861159 56.4451813087 44.7630324173 0.3965364462 264 32.7687531622 59.6345240798 52.030068515 0.450924223
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273 5.8804102686 16.2766743004 26.1455793367 0.4030229958 273 24.4180304793 53.5787874578 44.3457934277 0.311801745
274 8.0160906568 18.3880201054 26.7730016168 0.2021398001 274 7.9644474966 18.9527391768 28.0566445687 0.2224494102
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276 16.874866481 49.7933115277 37.2635476074 0.2744003118 276 35.758979917 73.1072577167 54.8619644042 0.2694344904
277 2.8364208182 8.2347375613 22.7198911049 0.3892700006 277 6.78624193 17.1796863919 27.4587381963 0.3233443932
278 9.1375988177 18.7038588108 29.862419783 0.2962766282 278 4.3102835433 14.4558398391 23.9997167639 0.6135505269
279 17.4279162605 31.7153438677 36.5647454883 0.3311446305 279 15.8324353746 33.4393462838 36.8542643961 0.3188769427
280 21.5358492596 39.4180338474 40.705255284 0.0659958448 280 8.3935119426 19.4175828203 28.2168167471 0.4659510355
281 14.8447893303 39.7729137192 35.5419303423 0.358871715 281 15.7949634192 40.6513103314 35.6991446057 0.3773880096
282 4.151965753 9.0347665534 25.2923248716 0.319475007 282 24.2442779961 55.6207522987 44.4678608578 0.2110914783
283 35.9218322732 59.6685832106 56.4643837952 0.2932651549 283 11.5053335885 32.000665266 31.6131544137 0.3815689289
284 4.5143404077 12.3068220851 23.5305200994 0.3548220977 284 41.038062785 90.4149903274 61.2252494956 0.0674898681
285 7.5394512519 23.8412500783 27.8980754528 0.2870257536 285 12.5458957963 39.7454004721 34.1435630892 0.3544506767
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287 7.5479354397 16.0518937595 28.4128102054 0.4056694987 287 4.3469841291 13.3783954583 23.2287043651 0.3420497378
288 10.4099774568 22.3286099371 30.5301337065 0.3917411903 288 5.2477263257 19.3857918487 26.8600811173 0.5316069937
289 11.4185548854 34.2546337972 31.0261882343 0.5669934796 289 6.6152894227 20.7645375295 28.6305059369 0.4118612954
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292 6.5372591148 16.8343298121 26.8833497301 0.4345948282 292 1.4296917173 3.583325821 20.0929509318 0.4652643135
293 6.518290004 15.4049142896 26.8253295164 0.1685084856 293 44.0556414492 67.0940663418 63.680426938 0.0325816026
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295 8.4227521098 16.5618031986 28.2003983674 0.4892882845 295 15.0782515847 33.7347279795 36.4544663077 0.259095995
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297 0.0710755923 0.0710755923 20.7364092584 0.6727145203 297 4.0314588252 17.8291123347 24.1634221053 0.304456754
298 9.1341891693 22.9720371649 27.8658293438 0.4932790564 298 20.8954401446 34.0692034948 40.9588804091 0.1514173467
299 18.6553659199 38.8909230235 37.8439774382 0.2434393963 299 5.9708185802 18.2778068572 26.4145158986 0.3850904355
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301 11.4473660644 35.7693962627 31.0910329016 0.424913203 301 12.3400585635 30.3841435131 32.6073945187 0.3333724853
302 5.5730960362 17.5985571301 25.6274168092 0.3018883985 302 18.9999647509 47.866743294 38.4445421276 0.0851300532
303 20.1248813673 39.7996567113 40.3340309885 0.3206236754 303 2.0942020075 4.6926366545 20.6995966009 0.5700016647
304 6.6042559353 17.2169385765 26.3042307969 0.3925352597 304 14.5763607812 37.4191154762 34.9835845986 0.2707483206
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307 4.2837321914 12.0118112594 24.9476092284 0.5311075822 307 34.9510664789 61.8335086408 55.0528269484 0.37763306
308 7.1162149636 17.7966371945 27.1031744467 0.3355371817 308 15.2655318207 50.3594047082 36.1320267469 0.1985066127
309 14.2778306059 33.2598077253 34.4314464786 0.4218938424 309 11.8210543759 34.6373588298 31.9490755781 0.346738022
310 10.5856240613 23.8851570523 28.8733391182 0.0473616278 310 3.2655697467 7.8876258698 24.5182830838 0.3703772469
311 7.0525950723 20.2708909155 28.2691514939 0.3373664107 311 1.3966749515 3.3566018394 21.1851656996 0.6241945919
312 5.2631411778 17.7201119666 26.688696556 0.3862431599 312 13.3041584107 27.6374909824 32.0989489559 0.2090335497
313 33.2211413942 56.3362211539 55.0630951471 0.0375539812 313 23.6979198046 40.5719274566 42.9505036871 0.3851826096
314 9.015309358 19.6759479989 27.962291544 0.3070409585 314 14.1420404004 26.2310650897 33.5203084816 0.151639097
315 8.1896055 19.9795594439 29.6053094428 0.2667770774 315 22.2615067838 52.5899784785 42.1486206789 0.3160545357
316 29.5540588913 63.5683130679 49.1230689772 0.2213032848 316 7.748718974 20.4124418068 27.9179572088 0.4381991616
317 1.0370171535 1.1246926182 20.7727412669 0.4936161443 317 9.3516692083 23.6649762591 28.3881581574 0.4130227969
318 6.6806852758 16.7963740513 27.6009786136 0.4987149958 318 7.2442385003 16.622649023 26.1784114672 0.4603139655
319 12.7567382634 38.0431406194 32.6355838973 0.3550552819 319 7.2145608522 23.820662982 27.9162666564 0.3439797195
320 4.7638545726 14.3995694206 25.9797605064 0.6075922612 320 5.0514899178 14.9419550321 25.8360992404 0.4238938215
321 8.5702814469 25.6073288876 28.8434406237 0.435663822 321 15.1731053678 22.2975854041 34.7519180962 0.1125911799
322 5.7527827561 16.7411457585 26.6095893503 0.6118074797 322 7.5080649159 21.9237141376 27.6288363927 0.4022965745
323 3.7346609641 15.1487835837 23.5871978365 0.4850971128 323 5.3527067085 15.598638848 25.0617190866 0.4439664936
324 8.7329979738 21.6410823592 29.2700358554 0.4613721748 324 28.8068419228 49.6025592528 48.6841323019 0.129970737
325 3.9847896882 10.6333476318 23.3079278187 0.5714099577 325 11.5878538645 25.2866185037 32.1801876318 0.2273278855
326 35.6353102442 60.3673117875 55.3973228143 0.0156803317 326 18.3335907859 35.9806765847 38.777388377 0.328257973
327 4.5878410595 11.15300628 24.0403824879 0.463186394 327 13.1332682274 33.1482976949 32.3505066659 0.1849407842
328 9.6317177265 22.7283538757 29.624461155 0.49895858 328 3.6165791994 10.5854661713 23.3309784343 0.3326760529
329 23.8074765164 47.6240869757 44.4717671733 0.2035984257 329 19.6662674013 50.8323477612 39.8439807721 0.4536361333
330 3.8372898374 15.7718365523 22.6379530492 0.5991705398 330 5.95814836 15.1185997763 26.3468428834 0.1877549573
331 4.7261746971 13.3021148782 25.1402088889 0.3189363708 331 70.7844064209 121.0057963166 91.9396402457 0.0812440525
332 3.9194053344 12.0569233579 24.4074250899 0.6823371079 332 2.1407213309 9.2505813827 22.4417662584 0.522394564
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353 19.5697920395 32.7355167534 38.7258944958 0.201712521 353 6.4824980746 17.4757161476 26.5266534686 0.3844663411
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355 28.0500965821 47.9177326876 48.3250456568 0.1741042097 355 14.9583675521 39.6556572844 34.6230495575 0.4840044433
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359 11.5441039621 30.1136367401 32.7006913203 0.3936200107 359 4.7658363875 12.8481419822 23.2753244313 0.5222473468
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365 5.7671655909 14.3441187759 26.0774648732 0.4521893399 365 4.3304772293 11.7697437382 24.3643599279 0.4282064662
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368 1.8870187551 7.4231706133 19.6764399827 0.6145116501 368 1.7338825848 1.7338825848 20.9401010747 0.5828378154
369 7.6542336446 17.9555990274 27.5488417412 0.4000243223 369 3.0777672786 14.2456172046 23.5853538681 0.5198344271
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371 17.2107575882 41.3321045126 36.7160725395 0.4629225809 371 7.9448609752 21.5878388503 27.911132395 0.3602335265
372 4.2067533032 13.8410423385 23.9202224997 0.4781338563 372 13.7384084421 27.3083780924 33.5087597414 0.202951562
373 6.8211987213 19.1103247254 27.4009197323 0.498877347 373 3.7419596531 10.7404091781 24.0891105061 0.1687806657
374 21.9366078176 42.3231826551 42.3429987988 0.0917618089 374 4.3691598372 14.6208439702 24.0069322915 0.3503739674
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376 9.9738095677 28.7256886935 30.9933349058 0.4657468932 376 34.303595593 55.9339081351 55.088515755 0.1677703086
377 7.5459242703 16.6542351175 29.4877107131 0.4473421488 377 50.6997630979 84.0577848818 71.4614754186 0.1168099491
378 6.328461444 19.651751816 27.0968876703 0.2519280387 378 2.7299700509 8.2319683486 21.4038886638 0.6120639184
379 8.0832820601 20.7733511359 28.8690515678 0.3139739238 379 9.1052255492 21.8041554534 30.388280558 0.416998472
380 25.4081075946 39.2182345858 46.191980829 0.1378149914 380 9.762974827 20.306279683 31.4498358371 0.2769543491
381 0.9542299075 0.9542299075 21.9003333955 0.5146286896 381 2.9788933034 9.1086888523 22.815233044 0.4199285217
382 2.2911979113 7.7525539585 22.2158251246 0.4638657182 382 3.126291157 11.9219175064 21.2774118684 0.4715086168
383 2.0805296754 9.7809645382 21.449958743 0.5294583623 383 7.256342217 17.3949040752 27.5030197866 0.3449026525
384 7.9576964034 19.4383565632 28.2027739546 0.433823159 384 11.3616373682 29.6360164356 31.6769344608 0.443834421
385 5.5609846122 18.6145351549 26.3662428072 0.4803851768 385 21.6741292527 59.6716409602 42.3817625277 0.3720870741
386 18.6623663826 41.7261330445 39.5177840799 0.1878259931 386 13.5563398339 27.4521662109 32.7747586565 0.3556773565
387 31.6374896818 68.6404716465 52.5640309655 0.2434435256 387 3.4982346019 10.5066695802 24.5365177825 0.6147698988
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389 2.1155368766 7.4207709169 22.5968529753 0.4140488093 389 19.3854899609 45.9010270697 40.2429714653 0.3582376668
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391 2.1868126993 7.8673488373 21.1203151018 0.5924532978 391 9.2153421655 35.6684824518 28.9879745506 0.566240606
392 40.0778579635 81.2577861971 60.861867836 0.1749286744 392 8.319810983 16.8018402272 27.0727203934 0.5140925234
393 3.5581909816 14.751819774 24.317276423 0.5147891733 393 5.4230636432 16.4753815891 25.9954082645 0.3508391209
394 27.6926278882 54.6470525656 47.7545500686 0.0333332554 394 4.8638299897 16.9537236383 25.3127723507 0.6096549084
395 25.2408050469 63.8627877923 45.4292122588 0.1022122086 395 3.3822842058 14.3251637117 23.5668531211 0.5506509576
396 7.6130880784 18.7861649756 27.6347074662 0.4514019772 396 12.3887051385 29.0213426358 33.8438563329 0.164998852
397 30.5387889568 58.3119003582 50.1484121685 0.1524537635 397 10.2322544703 25.0792934835 31.4277109395 0.4064352299
398 13.2401803522 34.6954530362 33.0119117041 0.3689360431 398 4.6146103784 12.2225184298 24.3466417615 0.4568307863
399 31.4360955853 50.330183875 52.0176165508 0.0297293949 399 6.7171875948 21.3755253738 25.6997360538 0.1708389599
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401 11.0217799788 25.0356625579 30.8764600819 0.3669687021 401 7.8908083126 26.0422499137 28.7081173195 0.4724329468
402 16.8871702587 30.8407524648 36.2002977203 0.0098714939 402 9.5222797278 24.5411834896 30.3436888036 0.3767424076
403 5.4202663423 15.702598002 24.960139514 0.6224909426 403 8.5534415682 30.4592969494 27.8457885499 0.1266745436
404 4.3854875191 15.2284014624 25.6454174518 0.6535905162 404 5.5556759316 18.2900513175 27.3340570293 0.3778796069
405 17.1936278987 43.5382000316 36.1522016996 0.4079778439 405 38.1914137859 61.8156881626 58.1717298961 0.1074326305
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407 12.2360967504 31.860534655 33.9118940068 0.4117841971 407 2.1896534594 9.6789499619 21.3592687277 0.562842973
408 7.2225075561 22.7468637474 26.937463933 0.4072294786 408 14.0440243928 29.8592031171 35.2101251884 0.1845947334
409 6.9200820957 24.3110291883 27.1411882812 0.4965930243 409 19.8138174706 45.2481257907 40.8251807422 0.3220872388
410 19.217032383 39.433765902 38.6082111445 0.4054273854 410 4.5491827154 13.8143034998 25.4939190992 0.4879965293
411 7.9225907284 22.9298499983 27.5976571306 0.4718057634 411 42.7998864123 72.1572389525 62.4850104101 0.2783284728
412 14.2652977828 42.2254352946 33.9484940731 0.4246124901 412 6.918241514 17.907961274 25.3930214064 0.3924602296
413 17.9220967259 30.3601111573 37.8985529808 0.2275045261 413 6.7316878652 14.5582509962 27.8813260592 0.3017005136
414 9.3018217309 25.2825397768 29.7888847804 0.3051010314 414 23.3922623725 41.7196349135 42.8934877084 0.0259182837
415 21.5446321713 40.6052479706 41.2539336964 0.3702162844 415 7.4799987065 20.418687396 26.6290086772 0.3157624555
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419 8.8595286493 23.2533893687 29.0873156698 0.4089387116 419 8.3513957277 17.5335148413 27.8063865354 0.36162173
420 3.6235418269 12.2040923223 24.3185193081 0.4924555368 420 11.8744851087 29.3714414213 33.3795157422 0.2212807374
421 15.8034522766 37.3165473508 37.6673443986 0.5389189988 421 5.6756066106 12.7078974929 25.4392258145 0.6635390631
422 19.5439791995 43.8075218468 39.2916691991 0.2532742229 422 40.2990507544 75.4775865379 60.4950878475 0.2571805252
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424 24.5434827236 45.7412480773 44.2824024836 0.1376922299 424 53.8303022999 89.8717999674 74.4294306312 0.3295314567
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426 8.4017234457 24.0281314286 26.699353295 0.2796579363 426 27.3796764444 43.2917410658 47.8184470597 0.0459394048
427 12.4118461711 28.3346008515 32.5217658439 0.4097371782 427 12.2425247928 31.3738137366 33.8268023297 0.4190258429
428 14.900931565 31.9012032333 35.184638876 0.2492238493 428 6.7845823841 16.7461198185 25.3724609569 0.4841395252
429 15.7795530479 37.7481526334 36.6805169112 0.2723164718 429 19.2840257416 46.178566552 38.3446205443 0.3006663446
430 41.7508298311 79.5291966895 63.7331345526 0.141639435 430 19.1491517628 38.4817952909 40.1998413674 0.2993229902
431 5.2131023731 14.2595005964 26.1199272864 0.3679918626 431 14.6624017002 41.5190414782 36.3891027088 0.4889499181
432 2.2989123856 7.1560629684 22.2846884235 0.7028670381 432 6.1188837482 15.7070285309 24.3106980641 0.5332059413
433 3.332372071 8.1314546378 23.0281671613 0.3718617042 433 22.7135460558 44.0547511104 42.0250407143 0.3094353722
434 6.9853207166 26.7889095659 26.0978925399 0.3593502865 434 11.0065388983 25.3751184144 30.4014937754 0.3255206014
435 10.5707788328 22.8235716744 29.8563187128 0.3696560383 435 0.1603356186 0.1603356186 21.5160504893 0.5182781277
436 4.1839876188 14.2015930967 22.6933715853 0.5602285175 436 24.1355360266 42.8909597097 44.9803500102 0.165991869
437 38.4465571974 59.0466406863 58.8601640095 0.0207789781 437 34.7996629264 57.3577274934 54.9972786942 0.157784722
438 6.4590404378 13.566352805 24.7800263169 0.4507525125 438 14.5837601798 28.9641724257 35.8393162635 0.1471016009
439 4.1872437056 11.3479564545 22.8289655098 0.4776851117 439 19.8752369967 58.6755972252 39.3369819581 0.466058108
440 10.0225473227 25.8880941061 30.1191781263 0.2142370101 440 17.1715876348 50.2662784689 36.6415923116 0.3243942392
441 10.7766887663 22.6995287304 30.0656999349 0.2386490425 441 8.0119762905 25.6689353225 28.7010033744 0.3303598459
442 1.6563572337 5.1296737309 19.7287372488 0.5289995313 442 4.4854736084 12.8607468467 25.8952249574 0.3606353089
443 18.6803674818 51.6817286391 38.4895274911 0.586761656 443 7.6828359778 18.3487571763 27.647513269 0.3936330069
444 9.2925148787 23.6516332975 29.8072830749 0.3002437892 444 10.1948868021 24.267971817 31.1034231421 0.2965896301
445 4.9670970042 16.6245308722 25.71204784 0.339149313 445 34.9834339928 55.2668643917 53.7815031912 0.0276885261
446 8.3681721169 18.4893649973 28.0410784327 0.2439608008 446 21.4351889113 50.3464558731 40.1594922229 0.2960983076
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448 2.2698928706 5.3683053012 21.525700226 0.4505076493 448 10.2260463215 30.9091426536 31.44301504 0.3581401105
449 5.002392466 15.0136744246 25.7253596183 0.5447905404 449 19.4040576008 40.7580011878 39.2728946658 0.2681042423
450 31.4668902298 53.1311844188 51.8840532627 0.2355267664 450 12.7962234604 36.3199316895 32.6944495002 0.5426778449
451 24.153534689 46.9791009788 44.6289879201 0.2307020062 451 8.6337746189 23.6947528827 27.5372030161 0.4161641129
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453 1.3252637152 1.3252637152 21.6797249075 0.5072534148 453 22.0850043609 47.011168573 41.2028775509 0.2664674296
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455 6.0848112965 14.6958727486 26.1753116455 0.3834694131 455 28.058652084 71.2785977869 47.4852574681 0.3967807105
456 3.2962243685 8.650565409 21.4152707372 0.6227567612 456 7.0471204335 16.8506780045 24.8720754005 0.4566950521
457 7.470001597 22.0039921177 27.9345904204 0.3988851768 457 14.0960910563 24.9117768589 32.9830706969 0.2003971674
458 7.2798107303 17.3275392239 27.7320656031 0.2987046515 458 12.4503953454 29.6435126206 33.7021182418 0.4637713541
459 2.6311989604 9.1029085967 23.1530106165 0.5533433815 459 3.062934949 6.2955569961 24.6609486161 0.2741099777
460 1.9938905524 8.117769943 21.315299305 0.4540567692 460 9.2140433976 31.4907897413 30.1927657295 0.4324740304
461 10.6292259426 22.2980665917 30.4818775067 0.5098245651 461 18.2308266336 31.9965234923 37.8786562798 0.3359210844
462 18.2398634506 38.2556322179 38.4293907253 0.5148159727 462 25.657297889 56.9326793761 43.9028458019 0.0093583775
463 7.4436227328 15.574003067 27.6522080283 0.2125600679 463 32.1044215302 63.4471359115 51.2711865083 0.2273089524
464 1.9525815154 7.1144171828 18.2330207551 0.6331132667 464 13.2881496032 28.2305656227 32.0672692004 0.1418951504
465 1.1792762185 1.1792762185 20.3936085811 0.6230824414 465 37.068696414 69.4134146306 57.0102708637 0.3488832483
466 12.4100981677 37.5675941372 32.8765360589 0.5875655515 466 7.5036321479 24.501081177 27.3016374409 0.5058653429
467 10.8841249574 26.4588419625 31.3036946986 0.2708507364 467 22.9776463086 54.9457307688 42.6959867898 0.4535578642
468 24.4202802756 42.9765061079 44.0762283479 0.2187817116 468 11.0766730562 35.396919676 31.1463734617 0.3533939908
469 8.0394026556 17.9737482327 26.5056648352 0.2847889562 469 12.6908613481 28.016802425 34.9949477935 0.1013346542
470 4.1940210347 15.600934337 24.2408277876 0.6165321474 470 1.9956491501 8.1383847361 21.8435459108 0.4898493055
471 4.6062456595 8.9585691415 26.152828729 0.3183755396 471 4.6297535946 11.347175792 24.849545503 0.5840150987
472 11.1653985371 33.1983394267 30.5808526682 0.4719275208 472 1.768007283 5.6314236671 22.2966112408 0.3982086452
473 4.3687209281 9.630988045 23.917561591 0.5042220923 473 6.3077111209 16.9426838303 26.156446147 0.1452413436
474 17.1848826175 31.2243628059 37.7006602335 0.2092822456 474 11.7502705301 26.4354043629 31.5725738962 0.190667672
475 5.8063328642 16.5259040561 25.2650843953 0.5265190792 475 2.8824806115 12.0340724388 23.0080466595 0.4682805859
476 1.6138918007 6.4607215128 21.7468205396 0.4064123147 476 7.0903214046 19.8548611313 27.3340357608 0.3524877859
477 5.649486144 18.5202641786 26.2432850775 0.4020993529 477 11.3528238446 32.6765288214 28.9105084802 0.445423274
478 6.9369296168 17.2274357409 27.3685955069 0.2732291013 478 8.850874715 29.506240136 26.9154379048 0.5126625637
479 10.0679688216 31.6769240792 29.2437096545 0.3476096526 479 6.4636361274 15.1810842445 25.4506607439 0.4963530458
480 9.1627195353 26.3390595725 28.546225555 0.6185159595 480 22.9804349643 40.4026099555 41.399676472 0.1530698398
481 4.3006878931 14.988082639 22.9787566312 0.5021103518 481 17.594227763 48.8731955175 36.8069126545 0.4904252978
482 5.7934086694 19.723478844 26.1216866614 0.4893420161 482 8.6918573273 20.8975667527 27.7976754791 0.2958026395
483 6.5890555645 20.9540339887 27.8853125105 0.3018065787 483 3.2746241825 9.9054999627 23.4918904174 0.6191683275
484 17.7529261269 30.9548827421 38.1174651498 0.3792549223 484 6.8288755663 14.7218539309 27.361080194 0.4190602765
485 11.2089180007 26.4875056813 31.3147410798 0.3290462366 485 3.503759115 9.6146479264 22.754307101 0.5147546647
486 11.6572675983 34.7594911778 32.3731491267 0.411818847 486 8.2393815186 18.7872244182 29.39098957 0.4262840284
487 8.0949406724 15.0357068279 26.576465295 0.5173527397 487 10.0064929206 31.8900618494 31.1328034546 0.3445840703
488 18.0966259954 31.7714923278 37.7202417517 0.2660887924 488 6.728247556 16.7091503757 27.7988117945 0.5376825865
489 3.4669435134 12.1205647924 22.095656488 0.4800854256 489 5.1809350027 10.6262040421 24.8888640285 0.2739505214
490 12.0955557643 30.4773379083 32.6911499643 0.4673395837 490 10.1036070674 22.1825051638 29.7318832125 0.2859132237
491 2.2284528529 6.7612077267 21.795657341 0.5380093578 491 4.3341586423 14.6779293585 21.9760034613 0.3303194395
492 20.5047724122 47.967423392 41.4996960749 0.3951661724 492 6.6429227531 19.9784593874 27.2183806176 0.2148789869
493 17.9034854442 38.5397245428 40.0033562598 0.459749247 493 14.247403851 29.3604033507 35.0276090773 0.1658594811
494 3.8348624333 10.4958865095 24.184368969 0.409303944 494 14.0778621316 28.6944138155 33.9032365126 0.3119320406
495 0.9167060858 0.9167060858 20.5102184914 0.6002465167 495 9.5618778721 23.2024044703 28.9163221883 0.3264409527
496 2.8626406537 8.340219162 22.9369169863 0.3794097132 496 11.9676345033 38.8464500027 30.8584564652 0.5143373749
497 3.6641305613 11.753538126 24.2462072535 0.4963307407 497 11.5035520863 19.4673853306 31.1827488819 0.1626092886
498 39.6926371742 85.1924473824 59.7023150665 0.0451607396 498 0.7132898069 1.6934999866 20.4789601806 0.6962454913
499 9.6341770478 20.923107986 30.1270422153 0.211973093 499 3.4979785404 12.2577889201 24.0934415409 0.2997733136
500 3.5730034172 10.577610909 23.1571752857 0.6430357745 500 28.5431494596 51.4956706204 48.5398152751 0.4435415259
501 7.8505720389 21.8454855885 28.4891712585 0.1124813665 501 4.4691925167 10.4127706092 24.8439729935 0.4036492485
502 11.1456449202 23.8619942763 32.0372863349 0.3340634595 502 5.5327340826 12.0059223523 25.2406226836 0.5005753482
503 14.6446108556 26.4299494999 34.4879061315 0.1912625652 503 17.7720982717 40.1980831914 39.1536156241 0.1251847875
504 2.5927595313 7.2512379979 22.494009702 0.5356173224 504 24.8147621314 54.9090324874 43.6680184298 0.1545442778
505 2.4471512521 8.014459011 21.9901490076 0.6399043408 505 7.336573469 18.9997667665 27.970751138 0.5402975085
506 15.2833176336 45.7925657557 36.3148925828 0.4961145894 506 4.2608514548 12.809644546 23.592783773 0.55167289
507 18.6073944025 35.468197651 39.325749296 0.3087676329 507 4.8851328799 16.3127758349 23.9571568179 0.4521025973
508 7.1981806737 19.3353395695 26.7451390753 0.6317408523 508 0.9369245126 1.0934066024 20.5583114095 0.5723541858
509 15.7636926908 45.2082997569 34.8030385965 0.2718168929 509 5.4425086024 16.6959309847 25.0554471741 0.5245755548
510 5.9351476816 18.8072082082 27.7041953079 0.5127533941 510 26.865789685 46.0633353111 47.9517433875 0.3394033956
511 8.9129227755 23.3276329754 30.0047577063 0.3298901525 511 5.3609686663 18.0196066593 25.053156065 0.5523738797
512 10.7690849705 22.5254499889 32.4427608831 0.1465835643 512 6.7841744537 18.3941534851 27.0657464865 0.4152045268
513 2.7240889856 9.3037272279 23.1155960752 0.7178776028 513 36.1061428708 64.4420404457 56.3673437103 0.0808787586
514 0.2757088658 0.2757088658 19.4686427673 0.5708386662 514 5.1891084281 11.8491548242 24.660171739 0.1773418698
515 0.6518505294 1.4991645428 19.4064217653 0.5084401453 515 6.5440028838 15.4046389821 25.1909287996 0.3293218894
516 4.3517490359 11.6437645152 24.5190306838 0.3258082679 516 5.2753642763 18.729045624 24.8418065492 0.6748242766
517 3.4361165789 9.4045180704 22.3109889233 0.3210396462 517 13.5861318704 36.4694095649 31.2314190918 0.3895549292
518 4.935980871 16.6051917229 23.9796634401 0.3558302867 518 10.2201462479 22.2288559864 31.7237165489 0.3420665341
519 7.3890398086 18.6621154375 27.1085711673 0.5341753739 519 7.2718151836 18.8591252165 27.0024502301 0.3681429536
520 2.8705041834 11.6762897394 22.7984793418 0.6086018903 520 1.8990090812 4.4901244639 20.8138781833 0.639132718
521 5.588428463 17.7997313799 26.18739659 0.4362629717 521 7.3914267226 27.8350180366 26.1330648739 0.527033982
522 3.9471459033 11.0417008291 22.8757098056 0.4445356564 522 16.4257301432 29.0594459157 35.7728720182 0.2728873228
523 15.6397205793 37.3222982267 34.9665213523 0.3220188328 523 4.8249550267 10.9334042317 23.854634634 0.3953563562
524 19.0050508425 42.6969873808 40.3867112674 0.374684307 524 43.7490980875 78.4053098562 63.8193051105 0.2588016785
525 2.4398192426 8.7166059686 20.7627077056 0.6028028508 525 9.5424312458 18.8189093543 28.3878399854 0.233691009
526 10.4314167877 40.09561464 30.9253005929 0.3637906907 526 8.2005469972 16.4913327115 28.2195881154 0.3943346431
527 9.5341464134 23.5585531649 28.1796655357 0.4108567694 527 7.7561847003 22.7940221818 28.5120483672 0.1506029002
528 6.8742078227 25.1996186712 28.9672267817 0.6201852892 528 10.8547466035 22.5493184554 29.7818445763 0.1208650746
529 10.6844784367 29.9751037525 29.8577425775 0.4099281863 529 4.8595220608 15.1687961529 24.5171773703 0.4632958785
530 47.0767395708 75.8459929726 66.7192680625 0.1879584073 530 12.7149191287 22.8565256722 34.3487911653 0.115230479
531 8.1181030331 23.1867853021 27.2760122714 0.5128316576 531 5.4345682798 15.3737070631 26.2187958667 0.3647705709
532 20.2672140789 39.4808317418 38.3969160275 0.1168764384 532 26.1648908843 65.8401642929 46.9559607716 0.1896399651
533 25.503314467 48.021078962 46.1542956569 0.3397893995 533 21.2420097688 55.0043875282 41.0562223172 0.2466974862
534 7.053338914 14.7553454096 27.0335195999 0.2920739946 534 11.5791953792 30.1906821839 31.0858262599 0.5522593441
535 14.3644413459 44.5116877445 35.1060607083 0.2008173699 535 4.4024856774 11.782975507 23.8277691591 0.43767798
536 0.4886512859 0.4886512859 20.6638937984 0.5921996814 536 31.50550026 48.3891069034 51.0895236275 0.029280657
537 1.7626590739 4.3600483973 20.5473443287 0.5710725955 537 2.8332411657 11.4443742423 23.2323972722 0.5054117179
538 8.0986112479 18.5445574222 26.6197961259 0.3692525089 538 22.3592777699 44.4518925407 41.9534921055 0.1179291433
539 10.0073845137 19.3158348305 29.7848495459 0.2477094399 539 12.2902945728 34.6992354315 32.7998255493 0.343770418
540 10.2287349255 22.1652347899 29.8694633951 0.3939292378 540 5.5653024906 13.8750362182 25.3344855844 0.3725522111
541 29.8881590645 44.4499755681 49.2498709528 0.0395668952 541 12.2449709808 31.2960478703 32.4089503056 0.2790775709
542 12.0326790679 29.4640153679 31.3514525351 0.3735454918 542 7.0017025229 14.2632904275 27.5150055782 0.3145478642
543 16.2147867708 33.3593756955 35.9631312426 0.2953025061 543 11.3236646834 22.5344157657 32.3013746661 0.5430237085
544 15.141699377 31.6004116546 35.6723746198 0.2181678771 544 11.2845602101 19.9151507497 32.0996315151 0.5577210546
545 20.4042119559 45.9587095975 43.5780735853 0.127645498 545 25.8347860447 53.2635238086 45.9936984824 0.1466953102
546 13.3421053591 32.0340365979 32.5528614785 0.1895778026 546 3.8007030594 10.9412841034 23.3238388951 0.6009499343
547 8.496797242 25.1559121586 28.4752795947 0.3649208738 547 5.2977431732 12.7480271052 25.4576741048 0.3926192647
548 8.8715419323 16.3843232904 28.6655961777 0.2308495519 548 2.7172242969 6.3601207943 22.7116173927 0.3980160462
549 3.3560282286 9.2522891694 22.9244907877 0.4648087938 549 2.3459185167 6.7794720975 21.7240452839 0.552601897
550 6.4852101482 18.4733170606 26.7897878136 0.417675453 550 8.2953531978 19.7799263678 28.2069007638 0.4039102904
551 34.8055094175 75.3064632638 56.210639821 0.3084054058 551 7.7017637714 19.0524188861 27.7023988184 0.3728949585
552 7.8625806909 20.4477507727 27.9666469262 0.4210287382 552 7.5934733442 17.439934858 26.7777694977 0.3696057659
553 2.2192220181 7.4921165984 22.826020308 0.5705578348 553 10.5706390138 27.3855034712 30.9411339761 0.4356594554
554 15.6946918295 24.923116217 35.3638529667 0.1081605946 554 0.4788818154 2.1516001387 21.7776167345 0.4164391388
555 10.4967164862 33.4526690741 31.2345205534 0.3336711681 555 3.2219004763 10.5977336044 23.0925598386 0.689640225
556 13.9607650169 31.6962852411 31.6326912598 0.2479243032 556 15.456221682 46.4077403492 36.8356664722 0.1658621036
557 17.8733818203 36.6303130163 38.0804310651 0.3164137592 557 8.5737428553 18.2820837657 29.4922062282 0.5092856137
558 7.3328307738 26.3038586816 26.5803011521 0.5757784474 558 63.004775088 95.7405886665 83.9005625138 0.0043180997
559 4.9131639269 14.0905046193 24.9825070131 0.5746163051 559 12.1791902495 27.4676943257 33.1415077918 0.329663919
560 5.6398962769 23.5359972917 25.2269048634 0.5099442761 560 10.5829547808 26.8812093536 31.431206403 0.3284912576
561 2.3941896746 8.8364941268 21.749203685 0.484388687 561 3.3988314229 10.7251725412 23.7241631386 0.5391739216
562 9.1838187707 22.4686471064 28.9287545862 0.281992253 562 0.5268218077 0.6457576074 20.1295923778 0.3851058184
563 3.1603722455 9.8333716389 22.203040971 0.5588612648 563 8.847045236 23.8988135491 29.888327173 0.4178314498
564 6.4952620615 20.8598720532 26.6103626669 0.6587459387 564 19.0400558262 44.9463346487 37.8452908299 0.4331450489
565 13.6575381762 30.9344946248 34.5318198283 0.2640716055 565 3.5679757321 14.9956364053 24.0415994202 0.3190204599
566 1.3490261803 3.2900187518 20.8875387394 0.4501176797 566 31.4017312565 69.333362498 51.3072095889 0.3410842514
567 1.5230362555 5.4029841615 22.3297459918 0.580811028 567 11.6551170096 27.4402419608 31.2756822516 0.5119647908
568 1.6185960274 5.0054286253 20.9670364449 0.4774163787 568 7.8825265674 27.0650459861 26.8536756129 0.2780706354
569 4.4179970222 13.4348634648 24.6569440843 0.4932968971 569 7.0685990343 19.7539828101 26.4825269774 0.4821800027
570 24.5013327586 44.9741184672 42.8264574546 0.2959256417 570 3.4078173713 9.4221928978 24.3189776886 0.4896288467
571 23.4879872535 52.7171191178 44.056639493 0.1589396639 571 4.9297513811 12.7325443269 23.5841830763 0.3945274547
572 4.0122377714 14.5084383007 24.5622971295 0.3776461513 572 11.6255283057 28.6180859201 32.0287198887 0.2985500247
573 12.2346786827 19.8545846097 32.1046038263 0.0276813249 573 4.9625097196 16.852536524 24.3545165814 0.1438947624
574 11.2855647666 23.1614688014 31.631735903 0.3129024346 574 14.8852126753 37.2320209199 34.9903971055 0.2687631316
575 4.6818689455 22.2141853733 24.0533718598 0.6354405766 575 8.7462538307 19.6745542691 28.0526105004 0.4465044781
576 16.4939259228 37.6368816483 35.6778301893 0.3860207671 576 5.4125015009 15.2034301029 25.0008009869 0.3504341384
577 7.0724301876 18.3803472906 26.1902195464 0.2509896775 577 10.5940834087 24.2164017163 30.8143414569 0.3203992277
578 28.4540296261 50.8320151094 48.344725925 0.3381142952 578 2.0595824498 7.3928312933 20.7562126228 0.6057019217
579 2.6378228383 12.6780300737 23.0795027284 0.7542500586 579 8.3501432516 28.0659647606 28.6559126337 0.5464534104
580 41.2140937558 80.5144213419 58.4184977056 0.1408343106 580 10.1690416493 25.611515061 30.7212556278 0.4563288984
581 22.2206964952 40.3768866488 42.074631116 0.0750341481 581 7.1814216842 20.164526936 26.646118401 0.5649291276
582 12.1979611065 25.7340952612 33.6448979694 0.2201761519 582 31.4800347672 65.9184640297 50.0014970827 0.1181884307
583 6.7946622405 19.5742504004 27.5435065009 0.6735553653 583 2.689656186 10.8756616575 23.1915900318 0.6432064664
584 3.811135321 14.290603574 24.1020925169 0.5999453309 584 6.3348286726 21.0389817477 26.9513254688 0.5820467762
585 2.7213104233 5.8226060115 21.8436668001 0.573135787 585 11.6980184011 32.1463473369 31.7289827809 0.4021583112
586 35.9704040201 70.1787546215 55.3712567407 0.190101838 586 16.0390412642 35.5083252029 34.1527254347 0.3693593285
587 6.4923100439 16.9348900396 26.3738856114 0.2506846338 587 0.7977173361 2.1284208199 20.5503198493 0.5581723445
588 1.8350423361 8.1762075026 19.5149882353 0.5304031748 588 12.6477006946 28.1091933492 31.6634379594 0.2766430257
589 12.4304234486 27.820065715 31.3862314297 0.3368540997 589 4.7722523967 16.2105930574 22.999385951 0.7190167347
590 37.5893247571 70.0057057657 57.7102485015 0.0410175437 590 11.2831438092 26.5479731435 29.6692102335 0.3318027865
591 4.059221766 11.2287823731 24.0403622347 0.4414746127 591 13.5325874166 24.6754026719 34.9193493463 0.1978229488
592 3.7544043595 9.8874266562 21.6522899208 0.6198015456 592 9.0073200378 24.3587494527 28.1505671611 0.2336276495
593 15.1910824036 35.883965194 34.8177665475 0.5142292715 593 8.2325506147 16.3937329964 26.9805409048 0.2711144529
594 4.8829572254 16.4015549537 23.4514792176 0.3832187339 594 19.2609929255 36.8016042816 38.1738453819 0.1361270048
595 11.4645680523 32.5170047905 31.2525013075 0.4392516572 595 7.7761575383 20.6096704468 28.2974054951 0.2652198731
596 6.7793699516 20.5741615329 27.9804547442 0.4580049987 596 1.6868304495 7.1000749691 21.8787214502 0.4672533082
597 19.2658078368 33.9183866265 39.5181724883 0.1550895009 597 3.5613690216 12.2976620171 22.7836637047 0.5739852295
598 20.9456950677 54.2181153853 40.4927827984 0.4214124936 598 35.9543411367 61.7578479337 56.8144590481 0.0981908681
599 19.4658751294 38.7446281822 37.582023196 0.561384968 599 21.5185882624 45.2271788116 42.298639943 0.3199930057
600 6.3991601164 15.5636648636 25.1691319491 0.2124693631 600 19.0791379246 40.1967979726 38.8896509303 0.2047775874
601 19.493717662 55.8409528711 40.1138379752 0.5005655686 601 7.4970179693 16.8683406722 25.4115081452 0.3950575648
602 16.7417877776 32.1628551912 36.3423762804 0.4212985115 602 3.7175929157 18.3924985002 22.9178972492 0.6072946049
603 7.8140264625 16.6274185401 27.1710272771 0.5890507966 603 38.0052826609 72.8754172689 58.7763681307 0.1052431751
604 1.8440053081 1.8440053081 21.7773269187 0.648359662 604 21.1765922317 41.5451425255 40.6357097693 0.3856416488
605 13.6665141595 21.2246235954 34.0078884186 0.0378736907 605 29.3352346521 64.3025594557 49.572498101 0.1920981546
606 1.8348000818 5.4932928439 23.5473052008 0.4298859908 606 3.7690462705 10.229766409 23.9845657458 0.4130536149
607 3.3095382254 12.3838188517 25.145660736 0.5265866561 607 1.7984956608 4.7947202266 23.2686337208 0.3733799309
608 27.3940882804 58.5739847662 47.3690697348 0.2425671769 608 4.6476319852 16.6787438348 24.3591146533 0.4806250834
609 7.3397116181 22.1706136574 27.0791247265 0.6067396638 609 5.9204984164 16.6257395781 25.7506324435 0.3663164431
610 3.1806327797 12.7129794869 23.799163419 0.62066473 610 1.3281279293 4.8600296387 21.2671068979 0.461633626
611 2.0213283903 6.8776674631 21.7821625084 0.360930694 611 15.4128383426 31.9992027264 35.3032701153 0.4462229002
612 11.5457708561 24.99808318 32.5510645874 0.2652969849 612 7.5555286552 15.7453100151 28.3186043457 0.1210037472
613 14.8412455105 25.6441035923 33.4727867992 0.2120213304 613 20.0977004714 35.8866853746 39.7192002517 0.1436180763
614 11.4187106487 23.9837200765 31.7660092409 0.1628622855 614 12.8025883566 23.2197583711 32.8519268858 0.5632281572
615 19.0213795673 42.1689759531 37.7303810252 0.2917999567 615 10.1909728579 26.3543060274 29.9542637143 0.4164485072
616 3.2541552479 9.8087098746 24.2299045489 0.1796659188 616 9.7280753338 34.802914912 29.7451100967 0.4810872179
617 3.9658559115 10.7477614875 23.6575431293 0.4788058108 617 17.6788401088 28.8509752466 38.2162283695 0.2267096951
618 4.2323378024 11.6834612293 22.8803496959 0.4875877427 618 51.1768911728 86.9712185275 70.8917749336 0.0151861038
619 23.738312455 37.8584456774 43.3784472679 0.2661506024 619 3.8698472033 19.3349911747 23.8271130813 0.5527103435
620 17.4647911708 41.4658014204 37.049530052 0.1787165081 620 15.2560451499 40.4418243781 35.512374913 0.3056216227
621 6.1669953438 19.4452515429 26.1121912741 0.5040729177 621 18.391762016 52.800163843 39.3218500383 0.1147675602
622 34.3247013198 57.4173195944 55.6612513373 0.0478503007 622 18.7214983024 38.2052383981 38.5386454476 0.3460778103
623 35.2501709234 50.8548636646 55.5496685604 0.0925628943 623 25.7624107207 51.035485022 43.4782161294 0.1808666231
624 4.6055539656 16.5246601721 24.0076750452 0.4192033369 624 14.5614883803 34.8194825969 34.686265454 0.3628965879
625 14.4217879262 32.5077949657 34.4678979438 0.0990759074 625 10.0749495064 30.1383532936 29.26527682 0.3816246793
626 8.1107730476 27.5147650335 27.4514761752 0.3173951495 626 4.2821335004 16.4495921774 23.905976742 0.6357381851
627 6.2046400681 19.9755630089 26.3990240622 0.4195560348 627 16.038119009 33.8999453926 35.6036882462 0.2210101978
628 19.0179646267 36.6067779175 39.2813872975 0.5172453129 628 5.9442206102 14.9905194952 26.3073791334 0.2535766701
629 28.9977505849 45.4666958889 49.1246733606 0.060494176 629 3.9889359597 16.6325429938 24.9071411988 0.3733864133
630 8.3788263947 23.3112991098 29.6395476226 0.3148090697 630 7.9602261677 25.2599431755 27.6121214401 0.556482628
631 4.5840120744 12.940968088 23.7196258522 0.2056070199 631 7.5622283141 18.649060179 26.4915720278 0.3342145228
632 13.2954643304 20.9137812083 33.9148972458 0.0888587092 632 11.3912182236 27.0832088971 31.3078988185 0.4533793201
633 4.8483051585 12.2780233426 23.6672026299 0.4422158745 633 3.2531137839 12.2942211807 22.7206941527 0.5622682988
634 4.7736837721 10.975565916 24.2210855176 0.3765747753 634 5.2142109161 19.5608335018 24.090778016 0.5776930427
635 5.4607915411 16.4849000095 25.1704825183 0.4224255269 635 21.4716215041 49.6586794957 42.2040843866 0.1014399739
636 2.5238593648 6.1144195953 21.0585561555 0.5127960482 636 2.7396476185 9.1318977629 22.5880869026 0.6022088498
637 9.9343666371 32.4929990828 28.7931894668 0.2946100444 637 6.069992061 17.2391799031 25.7888586284 0.4951208356
638 14.7403166307 42.4051325833 34.8484431898 0.3283301881 638 12.5332817886 23.1558433851 31.5496784166 0.3310112143
639 7.4502059334 25.0444960333 26.956781328 0.4976790271 639 8.349889234 22.0983268161 28.0187190784 0.3581087206
640 0.9061269022 0.9061269022 20.1547358533 0.5619199267 640 0 0 19.1780165873 0.6063175696
641 5.8578249359 15.317710898 25.1925471285 0.493004953 641 9.940539583 28.3813270588 30.1571051513 0.5942237588
642 11.8814649748 32.2625656196 33.0732908659 0.4383312903 642 7.6857654236 18.6856551397 29.0504830616 0.5479526377
643 8.6716209605 18.0987634301 30.0148069215 0.5951880905 643 11.8936922659 37.2288882138 31.1199839973 0.2780556318
644 6.6865484326 23.1860624578 25.1183407952 0.4302414302 644 10.6364840511 25.362365449 30.9751763341 0.395371239
645 3.3622955059 11.2052870637 22.4562370478 0.5383850908 645 4.2969405034 20.2954128402 24.5871932167 0.4688274058
646 11.498420269 24.7734852417 30.3843196623 0.1686518064 646 25.4601956033 60.8385525859 45.3096262719 0.3016997864
647 25.1175648173 40.3035750548 46.2910422374 0.0297471298 647 12.4259523565 25.6551051502 32.352768468 0.4308076395
648 5.2284754757 17.7150095849 25.6805235907 0.614761407 648 20.3526409231 35.8273805409 40.1499863005 0.4740597463
649 25.3861130896 42.0971126083 46.2263116118 0.0579461855 649 8.5565621918 26.6320530754 29.9867100413 0.351441409
650 15.3293793702 36.1785769459 37.014416958 0.3931087212 650 5.7383436492 23.9480032956 24.2326498287 0.6826490035
651 5.7586842051 24.3316310699 25.3163888937 0.4855279319 651 21.0251171969 29.2143493269 39.6923259578 0.0992019438
652 4.9824651345 16.5962182431 24.4529069944 0.5705038046 652 7.2798687033 17.7815647607 27.8868159108 0.2822145543
653 45.4632644168 67.5478597351 66.1648815629 0.2338088404 653 19.5021399044 39.5547590754 39.1248109284 0.3706850437
654 2.1874540025 6.1530923877 22.0503092663 0.6765266292 654 0 0 19.8660984936 0.6705346635
655 28.7700348296 48.5411836789 48.3873593687 0.1398433822 655 6.6162629256 22.431045911 27.558623347 0.5693092208
656 6.6838219691 21.8106900606 27.1251228091 0.4965041582 656 7.693347584 16.2607644415 29.4813058621 0.2369105766
657 4.7403734012 14.9372065921 26.582013904 0.3495313948 657 2.0462686812 7.7049585058 21.2439606869 0.6262909508
658 12.6483885891 29.9231691352 32.1656707632 0.5871235771 658 3.380353792 10.7822696302 23.4531391552 0.4519913344
659 4.6054129377 15.9976985552 23.382508152 0.5934248631 659 1.423201245 3.237328649 21.2995343541 0.6177787515
660 13.5217949316 28.4120224999 33.0092696455 0.4098543171 660 2.431554462 8.565300387 22.1343128365 0.4655595233
661 12.4571384659 23.1557642468 32.5957611817 0.3422715715 661 5.4578649147 19.1846456918 25.3427721372 0.4289666999
662 6.4677989748 16.6473175733 25.7855964279 0.2413119419 662 1.8230708046 1.8230708046 21.2895631077 0.5589547831
663 5.262827398 16.0433086694 24.325082052 0.4107680818 663 11.6137048945 22.1028584565 31.9711526907 0.262168032
664 3.3797113753 9.5842313034 21.9310769573 0.5759230504 664 18.2288623428 39.5926668104 38.2459498068 0.276505973
665 19.6139487904 51.2920332325 39.3646626926 0.2105545955 665 6.2732792955 15.2361311341 26.3741377485 0.5055527522
666 6.4107525732 17.8357761727 26.4980679698 0.2870118871 666 8.7551814275 19.0525677341 30.6118746361 0.3502976144
667 3.5774082517 11.2557618838 23.0848974211 0.3862673426 667 11.8100557229 35.6753884906 31.8157193602 0.398660947
668 6.5335164717 13.8177805254 27.2820168313 0.4378036584 668 11.9388187528 40.3465928062 31.6311034355 0.3071656916
669 3.3607609909 11.9229729576 21.4797929662 0.3855238105 669 27.487286366 55.8643018198 46.3196528291 0.0885629644
670 4.7233621027 16.0042241458 24.4309136169 0.4722380155 670 1.0002812387 3.0676064212 21.0857152232 0.4901179338
671 3.9568497099 13.8269569668 24.0763971045 0.2619445394 671 2.981689105 8.5459920399 24.1877340936 0.4952298042
672 14.4442283782 29.7041611317 34.4270315485 0.2799337836 672 7.3653794252 16.9180735895 27.8913405086 0.2713435693
673 6.5965515004 15.495371569 26.2822679831 0.4700611915 673 11.4168921155 30.9116159855 32.5932798522 0.3363337396
674 14.5858758402 32.2727109462 35.2927700005 0.2703465957 674 34.6374534885 67.5822997719 55.4304353365 0.3582327525
675 1.2293514813 3.360213108 20.6784143273 0.6160035151 675 12.0589069887 32.427860382 31.7702856539 0.4512512576
676 6.7446180971 17.9507470553 26.3723295925 0.4083834526 676 14.4773282561 32.8329252667 32.7710490444 0.5476462392
677 2.8049009098 9.6518184283 23.0519771275 0.548712268 677 16.6245785178 37.2360670329 36.6831187519 0.2661659049
678 2.9682661686 11.3313389052 22.072556688 0.4378501769 678 15.5215233644 43.1530188642 36.3372311769 0.3411318358
679 5.8588091268 13.4809395236 25.0474150943 0.3895270733 679 6.2003394488 15.128975248 25.598040709 0.4889440989
680 28.0465944924 57.3322331954 48.9818094969 0.2288152491 680 1.667773594 5.023984182 21.8640138321 0.4754407881
681 10.5066631773 20.0262494773 30.5960586188 0.1841402578 681 9.6030502348 27.4680994726 29.8540804967 0.4097797054
682 0.3051958109 0.9093221067 20.2739989657 0.5344317296 682 8.9951955765 27.4246174348 28.721627128 0.1362155281
683 46.018650069 61.4931652672 66.4109902902 0.1141368857 683 6.7838672981 17.1103532923 26.2669964189 0.4813422754
684 8.767723254 24.2746499106 27.5733972781 0.5260901711 684 13.3541382959 26.915004989 34.6231751408 0.0947877972
685 16.6873105212 29.6335816025 38.6113736189 0.047660487 685 11.5635017681 31.9548797949 29.9524917593 0.3546745991
686 7.8374269066 16.5312634113 26.5356906635 0.2792818072 686 12.0042025421 18.9967806051 31.0377885961 0.5308730214
687 9.0242485971 18.4402445865 28.3201190219 0.4029525407 687 16.7244047983 34.6341985448 36.0102151731 0.2318566067
688 13.9306655012 29.9325625336 34.807837216 0.1741046064 688 10.958955668 34.6890581361 32.8075816112 0.5640482126
689 4.0629364815 12.5089874277 24.9849804813 0.6490946645 689 3.2052463879 9.5372497262 23.0549904319 0.6111744557
690 26.8037727605 50.3984471939 45.1279628775 0.4299997954 690 7.2901987733 22.7425976833 27.1950730728 0.6351473764
691 2.5825120106 11.1136773903 22.0063725864 0.5386553218 691 1.9670790863 6.7793753856 21.3218165184 0.4616566225
692 6.9751258664 16.7838220267 26.9035237325 0.2666260787 692 4.6174761066 13.4086539775 24.9444841076 0.4081636809
693 3.8691140908 13.3388825499 23.1945896187 0.4864123887 693 15.9669004686 33.8142467185 35.7564943653 0.3245594554
694 13.1563720522 29.1521552545 33.4938584746 0.2146360113 694 12.4062807553 29.5354694981 32.4337434021 0.4153985159
695 18.5563052365 45.2430752054 38.8063948836 0.3351032828 695 5.0757131005 17.5398182394 24.8512282834 0.3571271799
696 4.7664147962 13.6383729918 23.8564362515 0.555410293 696 1.9716419777 7.94392109 22.5324396128 0.5601953175
697 11.4541868578 28.9239016356 29.4512973211 0.1552760984 697 46.8199888686 75.7304752673 67.5684077319 0.2448379706
698 12.3825993058 23.6517280226 31.8734995679 0.4626613557 698 10.2554010701 23.8658251646 31.2607859171 0.392716368
699 11.4438574047 29.1633545164 31.5376853404 0.3405281009 699 7.2809121613 14.3499388134 28.4602577674 0.355516677
700 6.5440466653 18.5035961719 27.1661124968 0.5390456028 700 9.8847140112 24.236520262 28.6142385324 0.4002319955
701 6.548006437 18.5761148633 27.534606163 0.565840455 701 5.8119179807 12.4847277601 24.1571795941 0.6351534066
702 11.6366807255 24.7752032826 32.1181198121 0.245474979 702 2.5496111477 7.020655861 22.4013587953 0.4716564931
703 30.5859238877 80.2026740257 50.1962441199 0.4024657631 703 5.0872467381 15.6674959011 24.0357236457 0.632683552
704 2.3681977969 9.7157238539 21.7082059458 0.3942581474 704 0.8234717773 1.8381809299 19.1803280402 0.5103410683
705 33.4164942233 55.6925476303 54.8921949739 0.1629751483 705 15.3794833916 41.4823339874 35.3404927239 0.4625185941
706 12.1056380191 27.4628334794 29.884795402 0.1536215457 706 12.8469192538 32.515844926 32.9042243096 0.3577615047
707 11.4839610808 21.4137062347 29.0213646155 0.5527767574 707 12.8293470074 22.8062929984 33.7821926273 0.2810820131
708 2.3559002965 9.7840565365 22.3995374741 0.447810521 708 7.9307440034 20.5268930322 28.2599562001 0.426575204
709 8.920779659 32.5109171173 28.1064167512 0.505124992 709 2.8811544559 10.5183678654 22.1596441969 0.4095382672
710 11.76040967 33.691585984 32.1349195509 0.6057869558 710 0.3732001001 1.3171011901 20.4829707483 0.4886644765
711 10.2808605064 32.9388201116 31.8274011516 0.4235441666 711 38.5756240599 72.0861513624 59.6143331855 0.2860889626
712 8.8066907707 22.5051234675 29.2126781031 0.4211493835 712 16.8999696216 37.6267689842 37.7129796318 0.0323804016
713 16.2870810809 30.8642772552 35.8504611439 0.2381091246 713 5.8315809934 18.2388928865 27.072583967 0.6392982831
714 9.8439678864 31.1268242322 29.105992128 0.6641907934 714 9.0989051933 34.2077693996 29.5314109687 0.4238853211
715 2.049895279 8.990481567 22.2491810791 0.3781719067 715 5.207024194 15.8958288342 24.4630690713 0.3286560965
716 14.6554445519 39.586153698 34.4954924139 0.390859684 716 9.3724409698 22.5155044936 28.845445695 0.4826396694
717 3.7305395767 12.6274315938 21.1555876014 0.5771585472 717 8.260995375 18.1432255356 27.9415875472 0.3806538517
718 5.6946419676 14.1203191296 26.3664451619 0.3864993065 718 24.8245821723 52.1175898715 44.7078846009 0.1793967354
719 12.3045058568 25.4254982338 32.0970513799 0.2001634164 719 2.5493311632 11.3034507758 23.6793637311 0.4844541171
720 10.8844543591 23.5389994804 31.049246677 0.3738956448 720 1.6307781343 8.0999895928 21.0971458773 0.5616862471
721 49.8937902314 72.591056233 69.8837055839 0.054572204 721 15.3576605128 30.7622267508 36.0191087628 0.1269519785
722 7.3688496922 24.8626701941 28.3226427873 0.3567403632 722 2.9144027982 6.510027712 23.3601963771 0.4754011657
723 20.3733065514 40.1528703028 39.4064882794 0.390601339 723 20.9219383124 44.6298690327 40.7283999146 0.4907087916
724 6.845368438 18.6996507288 25.5662533613 0.3730270383 724 4.9957449961 16.5289800896 23.7254483695 0.6158313494
725 8.0273118432 27.7280998255 28.6065449747 0.5196414995 725 26.2964040249 49.5779421078 47.0582888424 0.367017584
726 15.2410422746 29.0396234147 33.1221224572 0.1749915926 726 5.9082186468 18.7555685836 26.0496035108 0.4587980081
727 2.9242307816 12.6696942396 23.3086119443 0.6302403803 727 3.4585591884 12.499644965 23.9869038501 0.545427424
728 33.3381200459 57.3369304098 54.1718755503 0.1916003147 728 39.1943565032 69.5202848812 58.8661983856 0.0939255339
729 1.630156539 4.7196891124 21.2707919591 0.64685812 729 8.5070866075 25.2135854749 28.5698966464 0.5536504342
730 2.9388173076 7.7080681551 22.6960998374 0.4424584706 730 16.6962990453 37.3611572798 35.7172748772 0.1894756893
731 15.3666096792 31.1611836928 36.2856681633 0.1564126104 731 7.2685748763 17.5991081156 26.4838339855 0.3852153699
732 7.0198644536 16.0022358905 26.0556722273 0.280261589 732 3.2302788585 13.3043500934 20.6245909297 0.5153027354
733 24.2963641266 51.7290976687 42.9350004319 0.3421622292 733 4.5236002152 15.4926353972 25.0765375396 0.501999693
734 8.48900627 27.3447045565 30.1106976856 0.2328933095 734 1.298205562 1.298205562 21.8985284669 0.5820402559
735 5.5835324116 17.7378428717 26.8046216584 0.4876749113 735 22.6350732562 47.3236467768 43.0903775459 0.2344421461
736 10.5360663719 28.2398022057 29.4351717983 0.4971220018 736 5.452848236 14.8741531356 25.8992424037 0.6125404802
737 11.3547923448 27.0072917034 31.3539314689 0.3814366146 737 3.6138699425 15.4092467896 23.2295611489 0.5894107855
738 7.2662446299 18.6134081424 27.5659813335 0.2588328055 738 8.128610083 18.5844057928 29.6558825823 0.3194901556
739 22.573156584 39.2821833675 43.9906580474 0.2009243058 739 14.2700202547 30.0374496488 34.4092598842 0.1367201736
740 5.4336213325 15.6340227185 24.2498409596 0.5218792464 740 11.1978023205 38.209671957 30.7330716634 0.3333746486
741 18.0482047751 39.4754120694 36.3009103535 0.110507322 741 4.3664681877 12.8410396089 24.6797719069 0.535822829
742 23.3718074138 49.6063915247 43.0878763993 0.0618322668 742 5.1899813241 15.4837535018 25.4008176146 0.3466795502
743 12.096920096 23.8754484477 31.4081465804 0.0560635869 743 5.0063532987 12.9698950536 24.9194739648 0.5349047019
744 21.095475364 40.0067023007 42.2506229709 0.3808442683 744 1.611873526 4.7157421173 20.2644746881 0.3191329943
745 3.3369907284 13.9992745883 22.9948266917 0.4667114994 745 8.4392338443 20.0273178705 28.2668253679 0.4939794008
746 24.0496823205 65.3195828577 44.6054884355 0.369773492 746 24.0462132173 51.1906173264 43.2607112207 0.1785328617
747 5.3765104736 16.1226048986 24.5662048769 0.4483143961 747 2.0978268864 7.0206291145 21.5692727504 0.6032125307
748 17.0310003102 36.3122652067 37.3831250889 0.341617079 748 6.6428503381 18.8991165106 26.0490627007 0.2659990069
749 16.3731690175 30.2311989288 37.1272940793 0.116929668 749 6.571510949 17.9893401901 26.9909784026 0.4875354981
750 28.8073913805 54.5155149301 47.9072266647 0.2833398875 750 30.8861461194 46.4113568015 50.1660871824 0.1322503688
751 2.7196607012 7.6117964363 21.4604476852 0.5965263036 751 3.9135411286 18.1091163802 25.4094320448 0.4392370028
752 37.6708795746 87.2773538475 56.75236135 0.3381684632 752 7.8554403905 21.2078039738 27.9790464425 0.3441016533
753 8.0279525511 24.7811672145 27.0644777726 0.4012494267 753 3.4651121715 10.1882799611 23.4601127081 0.3771290168
754 26.8231564088 61.6479503513 47.6790251386 0.2891820893 754 2.7268942346 8.6075321384 21.9273562536 0.4861779621
755 11.5948755117 23.1696958359 29.1758164446 0.4502381187 755 20.7771372072 32.1030470519 39.8177221168 0.1398205097
756 3.6693578342 10.7481014943 23.4006116052 0.6942762757 756 17.1721146582 35.548558686 36.7666533223 0.5010602063
757 1.4904526554 6.873395097 21.6035048634 0.6833456411 757 6.8383359421 15.1590979827 28.4502559777 0.3895671214
758 11.0542562244 23.797007045 31.1734723748 0.3219566394 758 1.3949065056 3.8087618105 21.6886134196 0.5350964485
759 12.9720247138 29.9370281245 34.053286343 0.4755561868 759 19.348722421 44.1982893136 39.232512012 0.2643890715
760 5.479611256 16.3338851165 26.8282054222 0.4376581684 760 0 0 20.5876735758 0.4833445097
761 3.2117839412 8.6217417295 23.0064527276 0.4262698766 761 5.8477600596 18.5611848816 26.2816002812 0.5450779408
762 13.6049127852 34.1051942241 32.985385309 0.4044741886 762 3.9701386661 12.0856332726 22.7050410012 0.4527995382
763 25.4797391932 51.9111878374 44.2925107139 0.1783995509 763 4.7486434772 19.3365279402 25.2731114571 0.4487161688
764 3.8741162051 10.3032008061 23.9530024877 0.432762272 764 25.1420199524 46.2330535647 45.7914816154 0.3631293212
765 10.5870131915 29.8957480026 32.1856857605 0.3934269305 765 8.0712685919 16.6147646516 28.9352046514 0.3875634291
766 24.1505612202 65.1244165654 43.2015655363 0.2076600126 766 20.4888806052 50.7944118813 40.2046810647 0.4378360464
767 27.3985062827 56.4284190556 46.6873975856 0.1136502055 767 25.1007033465 54.9546831512 46.3820774444 0.0792440601
768 5.9404552058 20.5389122356 25.6951606124 0.4944673145 768 1.8929759796 7.9844179207 22.3238466526 0.4806639256
769 10.2259930261 23.5400944846 29.5542270902 0.3900023453 769 3.7715948222 11.4396627362 23.8710503168 0.3905956317
770 15.9354127515 43.3622923306 35.7213552774 0.4559014898 770 44.0500519502 77.4061007198 63.3966467258 0.0540439458
771 2.8002874514 11.2987885346 23.8398613104 0.6439776177 771 25.0263087076 43.059895997 44.1792296465 0.3250968279
772 6.8150109355 20.6166015361 25.7041039607 0.3259560614 772 7.6089122723 14.3856343437 27.7261226094 0.3850849462
773 5.2018913522 15.1101036422 24.6683932735 0.3925443116 773 9.3209544579 28.2889026706 30.0423154575 0.2638936141
774 19.3414815688 41.0863998809 38.0468861117 0.2607021625 774 28.0876013934 50.4402153099 48.8023517503 0.1347087839
775 14.2557944514 29.3498706189 34.7191104871 0.3087218504 775 34.9231399927 68.1001753454 56.2655918487 0.0791612652
776 4.6032131708 15.5924475344 24.0461172962 0.3744625632 776 3.664829616 12.1620054136 23.8204547979 0.2272200489
777 15.4450393202 34.7178081725 36.3881582593 0.3569901648 777 4.3016379174 12.8649716742 23.2167312453 0.4043309602
778 14.1929680668 29.1957976699 35.7439256814 0.0378610284 778 8.8249281689 19.0780800561 29.8975935749 0.159108409
779 2.6185948788 11.6835067495 22.5586234542 0.4992674174 779 20.4322194972 40.8119181591 41.0734041557 0.2444987532
780 8.5516744769 22.1780318321 28.6994513445 0.607045894 780 13.0591020829 26.9103158631 32.2395489765 0.3673011918
781 8.1615867212 19.183290097 28.9063594279 0.305908849 781 3.2143123803 12.8748547841 23.3238326465 0.6594560262
782 7.3171929083 17.3851449131 27.2881088675 0.3743719356 782 7.6857517255 23.4327728952 27.3868979586 0.3975812601
783 0.238084186 0.238084186 17.6084086456 0.7385362352 783 5.0661638378 17.4948745657 24.8353268706 0.3740546041
784 5.845095161 21.9999989406 25.9580850421 0.4059675912 784 14.4167137931 29.2178592087 35.5420515868 0.3168993315
785 6.3473533281 17.0565246689 27.0519986014 0.5192785524 785 12.3474345655 29.4521804234 31.7649217563 0.458120796
786 0.57912465 1.5182679748 18.5091325536 0.5548217453 786 2.8627520591 6.3863076998 23.327389044 0.2466975112
787 16.4912017825 45.0372247589 37.0812861846 0.3550645131 787 5.4277475582 15.4802697248 24.0761101663 0.3604486706
788 10.4804517404 32.6532655674 31.2138543087 0.3496837704 788 2.1823339019 7.3278433524 22.398195514 0.6275961808
789 3.9632242911 17.2920342413 23.9431753479 0.4604561389 789 30.2715130185 61.9600068499 49.9389282104 0.0558023311
790 17.8386673396 40.2313349877 39.160914108 0.1806657892 790 3.2592675296 11.4355307357 23.9210883807 0.6177412901
791 8.8494306192 17.7268825751 29.4749521308 0.1685674248 791 5.8655339772 18.8814537413 25.2165368815 0.5775590151
792 13.4977051995 35.334939415 32.1245130815 0.3917167126 792 12.9823502316 24.980768813 33.5885502175 0.3557744791
793 1.3323817396 1.3323817396 19.6040757804 0.6577113517 793 3.919135612 13.3155372561 23.8347646265 0.509334735
794 5.5045097184 13.280179603 26.4492868292 0.3985846982 794 5.8737955076 12.5459234281 25.0704304962 0.246546736
795 10.4343341409 22.3386965418 30.0498071913 0.5549845634 795 15.6293832816 34.6660176677 35.1568555922 0.2194836508
796 5.5169585894 16.0953150249 24.7735783624 0.1320872889 796 17.5879449723 34.0772414041 37.9996183503 0.0812949364
797 6.3400044306 16.1319368751 26.1922524534 0.3445011518 797 3.6039711045 16.3014976751 25.1186255852 0.4053365272
798 10.8787805605 29.0836165725 32.3777631549 0.4120732154 798 1.305199432 5.5106860256 19.5597992932 0.5210598406
799 30.5703305574 69.5038215819 50.0983509055 0.1617606289 799 19.1567383607 41.9799153358 38.8695458839 0.2636442605
800 11.720881206 36.3308469843 32.1826824039 0.5796643527 800 12.3747959125 30.4279614798 33.7787318884 0.3769978355
801 4.2335451721 19.8501516774 24.5201038107 0.343178825 801 6.6995182089 16.4694192744 27.3159809785 0.5931835425
802 8.304658977 16.9088017066 27.7354448287 0.364496561 802 12.7540638002 33.437208711 31.822805476 0.4293641916
803 2.5590642846 10.0687423728 22.5048306178 0.5360841035 803 18.7296526963 39.6602483289 39.2955273397 0.1561833199
804 11.4919580724 35.5540567748 29.429996604 0.2800535716 804 32.491502416 58.3777220855 51.9909878657 0.2415902407
805 11.6069634065 31.4359106723 32.9084300844 0.5213301854 805 5.9899927663 19.8188153693 25.4703530064 0.6016259334
806 22.4524417266 33.1634123523 41.4209727383 0.1086727444 806 4.730437382 18.6172933171 24.3962556097 0.4492532492
807 16.6012088312 37.1084419169 36.59700047 0.3061695376 807 17.5418838733 36.9857433751 36.5155137886 0.3385007465
808 41.6668900866 83.2961462049 61.1628666008 0.4922257949 808 5.0453589532 14.5458783118 26.1920188403 0.6395728004
809 3.3197987457 14.183567926 20.8714430091 0.568652194 809 7.2820126581 15.9829419399 26.4895136559 0.4728964044
810 11.971912266 35.038470564 31.4429330529 0.3897627413 810 11.7341899502 23.9635029132 33.2515153011 0.2403677618
811 9.3037000605 25.8293455384 30.7872913794 0.286017506 811 10.2697724694 31.9367815503 30.3100736364 0.352901799
812 10.6044445631 25.299442548 32.3241677063 0.2250163506 812 9.4212307497 21.8522521095 28.2408167444 0.2760381539
813 27.8207850185 51.1015947456 47.8804246251 0.0424949646 813 13.7456825723 35.6995531879 34.1944495337 0.1964206564
814 3.8373486074 10.3816625305 24.7044972987 0.1914406738 814 9.8623785248 20.7332654565 28.1036696722 0.2109677776
815 2.0082248233 2.0082248233 21.5066328063 0.6488839554 815 38.7542948577 81.9515053214 59.5367350168 0.1355405222
816 20.894944994 48.2229914901 41.5488886499 0.3114622502 816 13.1194666708 26.4435496317 32.9468080557 0.1883561674
817 5.3777368668 20.1912982079 25.3487747489 0.317277352 817 50.2312824676 75.1485413791 71.061554187 0.3095707965
818 8.9994378364 29.2742292031 28.3147408947 0.3077593902 818 4.8545366054 14.3354804453 25.2437868875 0.5982747144
819 11.8104393596 32.6201325173 33.3675836223 0.6591161612 819 1.3866200004 1.3866200004 20.033485126 0.4197392978
820 28.0781126238 38.298508935 47.3329972387 0.2093186556 820 3.7866241528 10.6966380868 24.995928057 0.5193592881
821 9.4609687925 22.6393124946 28.525103914 0.5603050405 821 8.0669317443 18.3775225312 28.1518217655 0.3742284599
822 11.380026849 33.0089130656 32.3714823011 0.5127297044 822 23.8642539455 48.0096553858 44.3498505876 0.2061403847
823 34.1343165147 68.3421953167 53.3784502783 0.2418988163 823 5.9349494554 18.0382636287 25.3591034236 0.5676578005
824 23.387316966 35.4051271851 44.4461430633 0.2623785689 824 21.0997416254 42.6566233729 41.3392383614 0.2235183436
825 3.318200179 13.2831734521 25.5594177454 0.5943045177 825 2.5410949809 10.1440472428 23.1352433554 0.4267330731
826 5.3869853505 18.0428520435 24.2360035318 0.5520233371 826 5.8323590271 18.4797291192 26.5219046433 0.3198600882
827 11.7915114738 25.9549521562 30.9832582331 0.3894435141 827 9.9901952614 21.7538389301 28.8848665412 0.3785166992
828 29.5595440561 58.3395661229 49.9073330759 0.2363000345 828 7.8699982106 21.5537295857 28.363293582 0.2126940714
829 8.2628987748 22.0120110104 28.9897958143 0.3148679378 829 20.8443102939 43.8254518788 41.192308445 0.0705770207
830 9.0382438673 31.2585648025 29.0840438166 0.3498214804 830 3.4961817777 8.6593277677 22.4908454317 0.2591997076
831 12.4798513169 27.0897970566 32.6946740279 0.3094923642 831 11.0875875161 21.2761658252 32.4291613452 0.1582676728
832 6.6544852786 18.5077330539 26.8122228294 0.4299386674 832 3.3419266013 10.4821573453 22.7133286398 0.2612962809
833 5.5869812326 20.6111720258 26.3136204687 0.4946875079 833 25.9098987831 46.3342104201 46.4183534788 0.0173561933
834 1.3251122891 3.7353617025 20.2378434374 0.4970628815 834 7.4934436706 15.3977365438 27.1667749442 0.2888071146
835 6.7856822492 15.1431483178 26.0506650776 0.4590681531 835 8.7950247665 23.9665432533 29.1447421042 0.3756888946
836 8.1805871768 25.4527426735 28.3760915041 0.5089458838 836 6.1931459785 17.667410036 27.1092540989 0.2743266361
837 8.554703079 19.7814822965 28.0768822255 0.4641643047 837 2.0635729144 5.6286440675 21.1537920754 0.621413856
838 5.8166393495 17.844478929 24.5604114405 0.4999068874 838 45.7369865024 85.9266908783 67.895093377 0.1961369561
839 34.0567247931 72.0665157798 54.7350165789 0.5512205132 839 4.1882889783 10.9861653605 23.614389015 0.4112605295
840 5.0642141465 13.6803754035 23.5102044492 0.5817393638 840 20.648477479 38.0501091698 41.3188113788 0.371147803
841 7.2482231436 19.4343388454 26.8276011727 0.3296258095 841 5.1533020606 13.72137607 25.7399302489 0.4327242214
842 3.0199264756 6.969054783 23.4573096969 0.4707003156 842 24.0753837667 44.9543903539 44.6478897633 0.0936706665
843 9.9619980291 22.6537327358 29.7400845536 0.3808760023 843 16.0818997536 27.1409361695 36.1206355999 0.2085274075
844 4.3573275295 14.9830750678 24.6232670774 0.5773713951 844 37.058147929 70.3710500124 57.7780826058 0.3488798663
845 3.0645692399 6.6203522948 22.7638790017 0.5338071538 845 10.7492346977 19.2963588234 29.9829646279 0.2218387142
846 0.9369682527 3.2871894774 19.2044761183 0.3171745065 846 3.2532997999 14.3209585749 21.6292942624 0.5421407049
847 15.5900684864 31.8312037029 34.6890094947 0.3535377454 847 7.7723370332 19.163729971 26.9578507597 0.5143758881
848 4.1981683716 9.0085867851 24.0151634485 0.2440748539 848 7.1793659934 18.0883926614 28.6015996119 0.2239085399
849 30.8410875706 63.2267896985 50.0046842126 0.3409171788 849 1.9271320307 4.8744098495 20.5715847928 0.5563877371
850 3.8711778953 9.8247518097 23.4924826966 0.4333807876 850 0.1133005252 0.1133005252 18.3096047457 0.5585194798
851 7.4275713362 19.5610979815 26.4164285651 0.5478699671 851 47.8886123043 77.0361476957 67.6400387689 0.0117569969
852 16.8470632991 38.177860622 37.8585448894 0.442173031 852 6.745532358 19.4993340994 25.9260871746 0.4553312592
853 9.8064288734 29.952888771 29.4860881821 0.2295376811 853 15.2908759429 34.1440767052 35.5377589576 0.3912809208
854 18.767292603 45.3565591993 38.3302686099 0.5034078324 854 31.872545581 58.7477793843 51.5050570022 0.2740075063
855 46.2553378992 81.1302407815 65.1417724068 0.1910762639 855 29.3229873872 51.1590658935 50.540231574 0.3132190486
856 16.5409414814 30.8191939806 36.4013096755 0.0853306966 856 13.8864993882 36.5443618916 33.7214671778 0.3376578129
857 26.2727978414 49.8268053428 46.8813844565 0.2069554073 857 41.0791899 77.2921070121 60.4865915502 0.1051448809
858 20.5711783111 30.4715791045 41.6143671885 0.2624173873 858 3.77494443 9.5586117519 24.1159301695 0.5339792443
859 8.3451546951 19.9377131733 29.1271473807 0.440362523 859 7.409923356 21.4241448438 28.9086206443 0.3890262821
860 20.9837188084 31.4922546052 39.2707617709 0.1824853153 860 11.3932136508 27.8879728893 30.5949615205 0.3810411386
861 18.5695454708 44.5251589047 39.0285312445 0.2326718686 861 9.0301652699 17.8087178031 30.4751020899 0.4420455591
862 19.8668243322 34.1761301481 39.2087733685 0.2613171161 862 2.4692909103 9.7748855041 22.656459906 0.5310620832
863 8.1542960526 19.6151493987 27.4672767249 0.3844698362 863 6.3553697405 17.0535440924 25.7495934815 0.345301577
864 1.7325602111 1.7325602111 20.7449191352 0.5764768955 864 28.321465424 53.7219620638 48.5097566787 0.0555526952
865 7.3200066941 23.0743674331 27.9612984374 0.4356354902 865 22.4976933112 48.0912856799 44.525161161 0.2771889319
866 12.3531258443 34.1247112762 32.9560465633 0.1889264422 866 16.9193245287 36.9256399632 37.4436965609 0.1621720412
867 15.8965228287 45.4301611551 35.7639695001 0.2945258423 867 13.8642089626 36.0405681606 34.4631449783 0.3392640049
868 20.7761981878 47.1232346618 42.4212493703 0.5021286242 868 6.9065370446 20.6339555036 27.4510352129 0.5151766466
869 25.9272476283 54.1383758574 46.5132581258 0.2322477283 869 11.4154177759 34.303925385 30.5818893652 0.4141635026
870 1.0319975582 1.6031917283 21.9415187279 0.5519330222 870 6.8450731009 17.5209919935 26.8871729674 0.3149860809
871 5.5115720328 14.2566607764 24.9729738286 0.4251346843 871 18.0808209332 32.5124944241 38.7354423797 0.162145106
872 13.8510317369 37.4280341801 34.322930531 0.4305918154 872 5.73968797 21.7206960095 26.149235761 0.5037431072
873 11.0599146993 35.3555319903 31.659636012 0.2028872777 873 8.8333553366 25.707981873 27.1304682674 0.2933969151
874 3.3235041141 9.279465747 22.2391859218 0.472457293 874 8.6684368836 25.972406754 28.3870514968 0.3933922123
875 3.6268555018 11.6360797903 23.6714925189 0.5403675041 875 14.1783965528 30.9283586115 34.7737721147 0.1816105795
876 5.0337527425 13.4203719505 25.0753928922 0.2497304278 876 6.5472663833 15.8392208895 25.6580085935 0.3245357152
877 6.6671191044 16.1888910367 25.1745075207 0.4353451187 877 22.2078346968 50.0123503829 42.4467707089 0.112684412
878 5.3869676113 12.9930730369 25.9177700376 0.5616499344 878 12.3710603182 26.4711655933 31.5760409941 0.3963133349
879 6.0756711728 15.5148036256 24.8176635209 0.3190382156 879 9.6245704131 19.3147897945 31.6861173557 0.3862696728
880 14.6412502557 46.2274625177 34.3629833398 0.3620439578 880 3.0793100405 9.9221453371 22.4197317485 0.510665244
881 7.3708861214 20.1478562932 27.6867465344 0.2940427525 881 4.0252967281 12.70925438 23.5448152891 0.2241593173
882 4.8424235174 14.3650721122 24.0792892819 0.5767201447 882 3.0496931812 10.5477559251 23.4097288821 0.5412618832
883 2.2428965 6.3966032037 22.4036719795 0.2684282079 883 6.4198578353 18.6927536335 26.3055489665 0.246839692
884 30.2292590378 57.9333068123 50.9167650611 0.2562942346 884 6.2384996 19.305662059 24.6907140066 0.547363467
885 4.8386082474 11.1830877199 25.3434051081 0.4393646486 885 0.4515450646 1.1679028845 18.2191906775 0.5281104469
886 11.8865116158 31.1266272615 30.9687409793 0.412817845 886 4.4863832014 14.9232866512 23.4357367399 0.4828481938
887 6.9664877319 21.764503721 26.3793045962 0.5094186713 887 16.8633169641 34.3004761807 37.4282827508 0.3903772636
888 9.4627303834 19.980141307 29.2421877018 0.5036229875 888 27.9424651632 44.4141209513 48.1416591852 0.1879993387
889 2.6580904467 8.453116238 23.2610091304 0.5380093537 889 1.3017141564 2.7261094051 20.3379382052 0.5320804833
890 4.9737909286 12.7378869606 25.4090480906 0.5200111699 890 2.5495311345 11.4596340123 20.9210914085 0.5639133387
891 2.3853622673 5.5567065001 22.8102470452 0.4696216547 891 39.6327300757 68.4357715515 58.2758036532 0.3900380418
892 11.6590154027 23.9829027917 31.6496473891 0.3405931033 892 6.9626692918 16.1115392215 28.4651970392 0.4635066544
893 28.9133822501 53.5498026863 48.2561529877 0.1886120567 893 13.5919974241 37.1159836437 33.9229010501 0.4166869059
894 4.720707487 16.6485651974 24.673407134 0.4936738501 894 23.8775613146 40.0119669746 43.7821908874 0.1223197064
895 19.0164769719 33.2363457096 37.3178981486 0.3739889609 895 17.0330985492 38.5790175368 39.4323194244 0.4090273376
896 8.9065613505 25.7587688608 28.6897278375 0.3295841629 896 24.7223863503 42.5649691057 44.3144846788 0.1536660127
897 17.1824720762 33.7007923436 36.0560699103 0.2830843253 897 6.4074604314 19.2011701778 26.9236909883 0.5600973899
898 5.234742577 12.6574420298 24.2596282104 0.4731246257 898 12.1505487087 28.2268683261 31.9914970066 0.4597765106
899 8.9965801674 21.7720008109 28.6308353588 0.1787283561 899 5.3740519841 13.7908996626 25.2326319154 0.3174537069
900 8.6074782416 27.556104852 28.7596520153 0.265665951 900 2.0313182525 4.9529875404 21.7922511731 0.3404888604
901 0.9316759826 0.9316759826 21.6295651557 0.5494366455 901 13.7200801089 24.9259521792 32.739346348 0.1994126679
902 3.7676422789 14.5243802262 24.1527719106 0.564014282 902 7.2137573859 22.6248553245 28.2965376089 0.5907754729
903 7.7431611851 19.6191808407 28.4625070975 0.5721823397 903 10.8665455216 30.2041513881 31.2583266776 0.498182139
904 10.4137438687 29.8221058896 29.9481944395 0.3946131327 904 3.7121894095 11.8262151413 23.9481040951 0.5077075779
905 8.4187713236 29.9585610457 28.7450525966 0.599121682 905 8.2808565407 25.1037207735 28.1025286762 0.3110930688
906 5.041802154 15.8124849532 25.1164907088 0.3292821257 906 2.102365497 6.4902804808 23.8196806627 0.5335405618
907 12.3087203111 22.7373930393 31.957432126 0.3348099054 907 14.2718210457 21.6377561304 34.960877576 0.01054563
908 13.0906295519 32.9602659913 34.1286758302 0.4366704586 908 16.7469420106 29.2360197261 36.5263297652 0.3277239201
909 9.2584128015 25.1395459396 29.9711155827 0.5472941666 909 4.2095049491 9.5310304369 22.6439689206 0.4883175759
910 4.2592864721 12.1415656002 24.2189148304 0.3670697822 910 6.9850131152 17.0413429066 26.1658708523 0.5871747459
911 7.3571566244 18.8436614397 28.7488962689 0.3379626203 911 4.5598174116 20.6400941111 24.2538371321 0.667076113
912 19.3210846977 43.0771313014 40.9559476953 0.3567240136 912 3.4277568954 10.7036854932 23.0714679958 0.4639865484
913 10.8747015015 23.6444473111 31.0468455692 0.2295006107 913 3.0262709749 12.2741806941 24.6727406236 0.4193180878
914 4.2521307329 11.6976060443 24.6193435349 0.4334023551 914 8.5553610352 26.2497217881 28.3204309505 0.5261817398
915 1.0303465354 2.8403333256 20.1389945223 0.5203832385 915 12.2280581757 33.2549984793 33.1806719066 0.2532644978
916 9.8454734049 22.0129328937 29.6563795428 0.1741508957 916 4.5071645848 15.9426555678 22.7300393005 0.3487421198
917 23.0664861048 47.6993977974 42.8860697075 0.3493382903 917 14.3467122076 33.6608201042 34.5142350384 0.2744506898
918 10.0785712062 30.9018231679 29.395311744 0.3013565787 918 9.8433283739 24.4588491275 31.05894272 0.3006319625
919 1.931038601 8.9581658477 21.0320238402 0.4413806195 919 1.4469999558 5.5368587028 20.8390329526 0.4916856248
920 9.5062517933 30.5838655473 29.3623368663 0.5262978169 920 8.9644764408 18.7427923138 27.9007442935 0.5007814698
921 44.916375422 78.763120876 65.8970254994 0.1901010421 921 10.2812594333 28.0253350919 31.1348589896 0.3607818995
922 10.6227351023 29.0895965625 29.3366212648 0.2073579047 922 3.7982093175 13.6364148669 23.6478937505 0.3818081681
923 3.6484676967 11.2089648211 23.8282392617 0.4599484958 923 8.6633928389 19.2677937867 29.7860227002 0.3009967026
924 9.4728499052 22.3301512883 31.0765877161 0.2355967436 924 2.6865006289 10.081636534 21.2418306846 0.5356143028
925 17.0893237638 28.7012044641 37.745968748 0.3540329716 925 5.2768326924 16.9108593813 25.3553287917 0.5971312587
926 5.0693844588 18.0133331437 26.0172478953 0.3532169922 926 6.5925923202 18.0333908518 26.3630733395 0.32027832
927 20.9377125887 45.6465060473 42.3837706441 0.1794249786 927 9.3453016165 21.5899845098 28.9484585545 0.4882704198
928 1.4277694532 1.4277694532 21.7118990502 0.4469425577 928 5.1402638252 11.6062966443 25.9354069825 0.4048527507
929 8.798542561 17.8411531552 29.1400110604 0.2447061981 929 15.1852420879 27.4558265907 35.7751815392 0.2178240951
930 8.2157679867 21.4628711874 29.7919683005 0.416561912 930 3.0710525903 4.262231912 23.6652577701 0.4803484045
931 17.4593803914 40.8011121435 37.3952042296 0.1025881913 931 10.1873923736 23.7758697234 30.7695710646 0.5310134924
932 2.4531022663 11.5647904284 22.6221530853 0.5380900943 932 15.030539277 30.343996007 34.0435318492 0.3079017639
933 4.1924622978 11.2527660456 24.7854598904 0.6387341146 933 10.1149620506 17.0195509582 28.4350949676 0.1711051828
934 8.7721608802 20.1413929118 29.5223622145 0.3251983588 934 13.8332460395 31.3310241693 32.9621211238 0.4156221507
935 12.7221927851 32.5871214469 33.3836970641 0.3548719326 935 25.6705443427 48.1653560616 45.5917680268 0.0259480178
936 9.2891454869 24.9478544329 29.2770332395 0.5131068767 936 4.007798891 11.392232586 24.3235393548 0.2641396556
937 5.9432480834 23.7440466756 23.7843552029 0.6016128042 937 14.0368499477 30.0616915666 33.8787753654 0.3893135111
938 21.4531691442 46.4216457698 40.868335274 0.422570898 938 13.2451106226 36.7358779912 32.4193762174 0.365889118
939 26.0166963953 40.1095104628 47.370151056 0.3334348734 939 2.8010120218 5.7533800935 23.7633879592 0.5163154547
940 19.9771634935 45.0370414334 40.6342150984 0.2380577786 940 3.1302479514 12.1949729383 22.3934140964 0.4450678818
941 10.1891378682 22.1662310246 30.3536203852 0.4035882343 941 6.8174699229 13.5297790931 27.0743592153 0.317081373
942 3.4570970735 13.4095884316 22.636413522 0.5116953367 942 7.6955169515 21.4705273147 27.1444189934 0.3532961114
943 5.0014516931 14.262451669 24.1985731397 0.3318187659 943 19.1608427934 35.5597044234 39.7283840668 0.2738217138
944 16.301528677 34.9505291847 36.2032891405 0.3552469944 944 20.5615359095 39.4714707342 41.1490708655 0.4192244511
945 5.7216549838 17.8715536359 25.1678697127 0.5217236819 945 7.2500734418 17.9259152313 26.1938693586 0.1978681914
946 9.5914273926 33.4672293984 27.7716833895 0.5056064985 946 5.1766144371 19.5479066593 26.9939694075 0.3061485402
947 38.8572336637 74.5597747584 58.2568667675 0.2388265118 947 8.1830628307 22.2030629726 28.5723550299 0.430973
948 1.9127246465 1.9127246465 22.6918521369 0.5792545606 948 7.3733117278 20.3646385337 28.0526456073 0.3972054484
949 9.5119730158 25.9949662362 30.1026655074 0.3074516768 949 5.7966549604 12.4389991844 25.9914162833 0.6085103241
950 5.0574525261 15.0114355119 25.1743045202 0.5690538016 950 7.6705765396 14.1463981263 25.7772325347 0.4669748715
951 28.0928347232 50.0019128005 47.985785755 0.0695621176 951 6.9900705199 15.2592102804 26.4427011141 0.1994699477
952 14.9322059483 35.1266007968 35.3802240736 0.2003558007 952 16.6584226799 27.2754772244 37.8567514385 0.1347151044
953 7.6942669254 24.0801484951 27.5708040921 0.4123207872 953 14.0682383795 29.5383095932 33.9230294977 0.2090841496
954 3.7648046778 9.4338053576 23.541236813 0.3045001214 954 8.1770286678 23.4094781893 28.2029107628 0.3948821002
955 1.0525739645 1.0525739645 21.9101940234 0.684662957 955 1.6528468474 3.8830693839 23.7734763599 0.3585124006
956 1.0432808112 1.0432808112 21.4892540092 0.7263063135 956 8.4367449895 22.0728763934 27.629519289 0.3838521732
957 6.8910258433 14.3140886423 26.6677035412 0.3523123991 957 4.0037033783 17.5012738765 24.9447537479 0.4635417156
958 13.8554761653 38.8100892567 34.1775360269 0.4121752465 958 6.022622643 15.7321089913 26.8283500348 0.174581632
959 12.6582504542 27.4643632988 31.7223187482 0.289576231 959 4.0462336018 14.7444232363 24.1547014866 0.3265890132
960 15.5618800504 33.6459105585 36.0276857883 0.1870375997 960 9.5232007723 27.8056932847 26.8426288314 0.3910615355
961 8.5070081517 18.522198088 27.7139035572 0.3925900156 961 32.3144517671 57.3414898343 52.0365303145 0.0419552865
962 4.9453528266 11.9057607629 25.3874310452 0.4739392457 962 4.4881277586 14.7687586078 24.8802347715 0.3251285589
963 5.4684516236 16.8161357534 26.2625702887 0.6379969417 963 26.1036285231 46.3515213654 45.0768931358 0.3696065014
964 9.1781553602 19.3359464805 27.4004110864 0.3725093334 964 18.9585378161 41.9611726236 38.8191609462 0.2683462124
965 2.7138031854 12.0842062376 21.4368219052 0.59917449 965 18.9022387193 40.0934434203 38.7085245144 0.2861508952
966 15.9046439373 40.0691523502 36.3313054002 0.374389556 966 4.5813440901 13.4463507846 23.9914311376 0.5123560766
967 10.352498588 23.8009215378 29.938339536 0.4758052439 967 8.752208833 20.3625998026 29.7882759838 0.5112168385
968 9.6000328605 25.9710892039 31.1568972884 0.3453721956 968 12.6747549185 32.4719346684 30.9842396189 0.3539209392
969 3.209500234 12.2043208932 23.5208704082 0.5082874584 969 27.4985431363 60.6436445766 47.6230305303 0.2587729568
970 7.8554022419 19.0745311313 27.683668846 0.3584287786 970 5.6366072023 16.0151985028 26.5833610134 0.369432406
971 8.6707097235 22.6008545955 29.9487875813 0.4024753893 971 9.2894223649 24.8979963383 29.4337406391 0.2340100496
972 7.9305752913 19.6012664815 28.4139929274 0.4694412229 972 12.4386018674 26.6712110326 32.912407293 0.1184872676
973 4.1100580858 14.5004686845 24.1962315352 0.5361135415 973 14.5138174596 29.6903121537 34.450460239 0.1829056396
974 7.2481948051 17.8201777199 25.5801013273 0.4580908403 974 14.2835861775 45.5196489467 33.7932547425 0.2749280238
975 5.5896567188 18.4419762508 24.6328405408 0.3939670707 975 11.0023555899 27.1828853158 31.4893036196 0.354842072
976 7.6144167592 16.0736490379 28.2323113874 0.3925129004 976 6.360484209 17.4572986818 26.3675703591 0.6267337903
977 12.4499028351 29.9470769454 30.804595053 0.1875612229 977 7.1628435165 21.2615606949 26.8865696052 0.3459561281
978 3.4748118652 8.513371899 24.1362545415 0.4607047933 978 1.9670365312 8.3280411946 23.4416657054 0.6128019039
979 34.364022537 60.1945918974 54.8662995802 0.1507752624 979 5.8968742069 16.4129000224 26.4412534708 0.2977945741
980 16.0058798577 29.2224168649 35.8660987491 0.3219028712 980 25.6973472726 52.2760246537 46.0440716292 0.4960133813
981 0.2304339063 0.2304339063 20.82926496 0.5749136991 981 10.0753250586 22.1202852339 29.6386398634 0.3441676457
982 7.9735204862 19.7674413032 28.8639847098 0.5049490315 982 15.1996212648 38.6802013689 35.5176517088 0.3955464622
983 18.6155316648 30.9539774759 36.8542498899 0.3175089086 983 4.935394656 12.3934612019 25.2624582119 0.427101097
984 23.344168468 42.6500280519 44.7535467037 0.012088475 984 8.7254105406 19.8794613992 27.5006306663 0.5063902894
985 7.6618410909 16.482946349 28.1926213803 0.3686055347 985 2.3541368173 8.4687050083 23.1301630085 0.6890070257
986 26.0299186026 51.7875759962 47.0383144453 0.2223170154 986 9.6653606182 23.0807308735 29.8594190583 0.3239495514
987 5.6292480524 14.6385863882 25.6689327591 0.4544322568 987 0.2686627106 0.2686627106 20.9776885921 0.6103053307
988 7.5461694123 14.2162422503 27.2186826522 0.4167914448 988 11.2813417658 28.0986663444 30.2479370265 0.5275567853
989 18.5943198275 56.2592989994 37.7999011106 0.3348128073 989 14.9504308729 39.7931368398 34.5656732553 0.3679180753
990 7.0626868231 22.7065322481 27.3006716498 0.4615996691 990 3.3176675925 12.2867731306 21.9733303859 0.4991681954
991 5.6428125144 14.3705190317 25.8714656849 0.4691876797 991 15.6013450292 34.621293096 34.6214616865 0.2553258112
992 8.21680117 19.3208917074 27.2232057212 0.5139161877 992 6.6457346538 17.279278302 26.5296696126 0.3236231376
993 51.7833963461 83.1821130205 71.1590976622 0.1974551932 993 9.4542572822 24.0264676133 27.4832125201 0.5044883283
994 2.9048149473 8.4819117309 22.0455702876 0.4743551885 994 11.8136882476 28.796885327 32.6752227305 0.3534765698
995 7.0667243912 19.3122237241 26.3079505083 0.4605566661 995 10.8624921177 22.1842311859 31.1848598819 0.3477684835
996 13.2311926554 27.4830693426 33.8986531969 0.4865479571 996 10.9470986173 26.9927685698 30.6145075117 0.4364973485
997 13.9928808843 30.9177449952 36.2103416428 0.5121007673 997 27.9488311321 65.8324138749 48.4415142055 0.5772834824
998 14.712550782 30.6729564177 33.7955754056 0.0611487421 998 8.0016792951 23.0558922978 28.2155895268 0.3614372535
999 3.4097603116 9.9091777705 24.4824219882 0.475058548 999 7.4187022632 16.2700739766 25.1111717224 0.5128496245
1000 27.5990148367 46.3153239921 46.4607866248 0.168629031
mean = 11.3

Risk Profile - Avg Wait Time (mean = 11.3 min)

0-5 > 5-10 > 10-15 > 15-20 > 20-25 > 25-30 > 30-35 > 35-40 > 40 0.56499999999999995 0.18 0.11600000000000001 0.05 4.2000000000000 003E-2 2.1000000000000001E-2 1.0999999999999999E-2 1.4999999999999999E-2 0

Avg Wait Time (10 customers) - min

Proportion